KEARSE, Circuit Judge.
Plaintiffs St. Paul Fire and Marine Insurance Company (“St.Paul”), The Durst Organization, Inc. (“Durst”), and Four Times Square Association, L.L.C. (“FTSA”), appeal from a judgment of the United States District Court for the Southern District of New York, Kimba M. Wood, Judge, (a) dismissing their complaint in this diversity action seeking reimbursement from defendant Universal Builders Supply (“UBS”) with respect to the collapse of scaffolding on a construction site, and (b) dismissing UBS’s third-party complaint seeking a declaration that the third-party-defendant insurance companies are required to defend and indemnify UBS in this action. Pursuant to Fed.R.Civ.P. 12(b)(6) and 12(c), the district court dismissed the complaint and the third-party complaint on the ground that the claims are barred by provisions in various contracts among the parties. On appeal, plaintiffs contend that the provisions relied on by the district court either are without effect because of a contractual breach by UBS or are unenforceable as a matter of public policy. Third-party-defendants TIG Insurance Company (“TIG”) et al. contend that to the extent that recovery is sought on behalf of Durst and FTSA, diversity jurisdiction is lacking, and that, in any event, plaintiffs lack standing to challenge the dismissal of UBS’s third-party complaint. For the reasons that follow, we conclude (a) that diversity of citizenship is lacking, but that that defect should be cured by dropping the nondiverse plaintiffs and leaving St. Paul as the only plaintiff; (b) that St. Paul lacks standing to challenge the dismissal of the third-party complaint; and (c) that the district court properly dismissed St. Paul’s complaint against UBS.
[77]*77I. BACKGROUND
The facts relevant to this appeal are not in dispute. The matter arises out of a 1998 accident during the construction of a 48-story building at Four Times Square in New York City. The present controversy concerns insurance obtained in connection with the construction project.
A. The Parties and the Contracts
In 1996, Durst, a New York corporation, and FTSA, a New York limited liability company (collectively the “Owner”), entered into a contract with UBS, a New York corporation, calling for UBS to be head contractor for the building’s construction (the “Contract” or “Construction Contract”). UBS’s responsibilities included constructing and erecting a scaffold system and hoist tower (collectively the “scaffolding”) to be used in the construction.
The Contract contained an Insurance Rider (or “Rider”) that specified, inter alia, the parties’ obligations with respect to the procurement of insurance coverage for the project. The Rider required Durst and FTSA to obtain a “Builder’s Risk policy” that would insure against risks of physical loss or damage to buildings and structures to be incorporated into the project and would cover, inter alios, Durst, FTSA, UBS, and all subcontractors as insured parties. (Rider § 1.4.) The builder’s risk policy was to contain a waiver-of-sub-rogation clause, i.e., a clause in which the insurer waives its right, with respect to a claim it pays, to seek reimbursement on the basis that it is subrogated to the rights of the insured; the Rider required that the builder’s risk policy “waive the carrier’s right of recovery under subrogation against ... all Contractors and Subcontractors whose interests are insured under such policy.” (Id.) In a “Subrogation and Waiver” clause, the Rider further provided that the “Owner ... waive[s] all rights” against contractors and subcontractors “for damages caused by fire or other perils to the extent covered by insurance obtained pursuant-to” the builder’s risk policy; that the Owner was to require contractors-to execute “similar waivers ... in favor of all other parties” that executed such waivers; and that contractors were to require such waivers by all levels of subcontractors. (Rider § II.8.) That clause of the Rider also provided that “[a]ll certificates ‘of insurance shall indicate, in the special items Section, that waiver of subro-gation has been endorsed to the insurance policies.” (Id.)
Pursuant to the Rider, Durst and FTSA obtained a builder’s risk policy from St. Paul in 1997, insuring Durst, FTSA, UBS, and others working on the project against risks of loss or damage to project buildings or structures (the “St. Paul Policy”). The St. Paul Policy provided that Durst and FTSA were allowed to “waive [their] rights against another party in writing” prior to any loss to the covered property. (St. Paul Policy § Y.G.) As indicated above, the Insurance Rider contained such a written waiver.
In addition to requiring Durst and FTSA to obtain the builder’s risk policy, the Rider obligated them to obtain on-site general and excess liability policies for all third-party claims. (See Rider § 1.2.) In accordance with that requirement, Durst and FTSA obtained an excess liability insurance policy from third-party defendant TIG (the “TIG Policy”) covering UBS among others, and obtained a commercial general liability policy from an insurer that is not a party to this action. The TIG Policy provided that TIG “shall be subro-gated to all of [the insureds’] rights of recovery against any person or organization,” and that the insured “shall do nothing after loss to prejudice such rights.” (TIG Policy § IV.N.)
[78]*78The Rider required individual contractors such as UBS to obtain “Commercial General Liability insurance” with respect to “Work away from the Project Site.” (Rider § II.3 (emphasis in original).) In accordance with this clause, UBS obtained from third-party defendant AIU Insurance Company (“AIU”) a commercial general liability policy (“AIU Policy”) and obtained from third-party defendant Royal Insurance Company (“Royal”) an excess liability policy (“Royal Policy”). The AIU and Royal policies provided that “[i]f the insured has rights to recover all or part of any payment we have made under this” insurance coverage, “those rights .are transferred to us. The insured must do nothing after loss to impair them.” (AIU Policy § IV.8.; Royal Policy § VIII.12.).
B. The Scaffolding Collapse and the Present Action
In 1998, the 49-story temporary scaffolding in use for construction of the building collapsed, resulting in one fatality and causing extensive damage to the site and surrounding area. As a result, Durst and FTSA had some $20 million in property losses, including physical damage to real and personal property, emergency and stabilization costs, loss of rental income, and the costs of construction delay, work stoppages, and extra interest. Durst and FTSA filed claims with St. Paul under the builder’s risk policy. St. Paul paid them approximately $19 million.
St. Paul, Durst, and FTSA commenced the present diversity action in 2000, describing St. Paul as subrogee of Durst and FTSA, and asserting claims against UBS for damages resulting from the scaffolding collapse. (Claims against a second named defendant were later voluntarily dismissed.) The complaint alleged that UBS was liable on theories of, inter alia, negligence, gross negligence, breáeh of contract, breach of warranty, and strict liability in connection with the design, construction, installation, inspection, and maintenance of the scaffolding; plaintiffs sought damages in the amount of $20 million, plus interest.
UBS filed an answer denying most of the allegations of the complaint and asserting as an affirmative defense, inter alia, that the claims asserted in the complaint were barred by the waiver-of-subrogation provisions of the Construction Contract. UBS also filed a third-party complaint against TIG, AIU, and Royal, requesting a declaratory judgment that those insurers were required to defend and indemnify UBS against St. Paul’s claims.
TIG moved pursuant to Fed.R.Civ.P. 12(b)(6) to dismiss both the UBS third-party complaint and plaintiffs’ underlying complaint; AIU and Royal, after answering the UBS third-party complaint, moved pursuant to Fed.R.Civ.P. 12(c) to dismiss that complaint, as well as plaintiffs’ underlying complaint. UBS joined these motions to dismiss plaintiffs’ complaint. The ground of the motions to dismiss the underlying complaint was that Durst and FTSA had waived their rights to recover for losses covered by the builder’s risk policy and that St. Paul had waived any subrogation rights. Plaintiffs opposed the motions to dismiss the complaint, contending principally that the waiver-of-subrogation clause was unenforceable on the grounds (a) that UBS had breached the Construction Contract by entering into insurance contracts with AIU and Royal that did not permit waivers of subrogation, and (b) that New York law, as a matter of public policy, prohibits a contractual waiver of subrogation with respect to a claim of gross negligence.
C. The Decision of the District Court
In an Order reported at 317 F.Supp.2d 336 (2004), the district court granted the [79]*79motions to dismiss. The court rejected plaintiffs’ argument that the waiver-of-sub-rogation clause was unenforceable because of UBS’s alleged failure to obtain waivers of its own liability insurers’ subrogation rights. The court noted that “the Rider sets forth a requirement for a waiver of subrogation only in the [builder’s risk] Policy, not in any additional liability policies.” 317 F.Supp.2d at 340 n. 9 (emphasis in original). The court concluded that the “comprehensive waiver of the right of recovery” in the Rider and the waiver of subrogation clause in the St. Paul Policy “demonstrate St. Paul, Durst, [F]TSA and UBS’s unambiguous intention to prevent actions such as this one.” Id. at 340-41.
The district court also found no merit in plaintiffs’ public policy arguments. Observing that “[njeither the New York Court of Appeals nor any lower New York state court has decided whether a waiver of subrogation clause” is permissible with respect to a “claim for gross negligence,” id. at 341, the district court concluded that the New York courts would permit such a clause, see id. at 342. The court reasoned that although New York law forbids a party to exempt itself from liability for its own gross negligence, which would leave an injured person without compensation, New .York law does permit a party to insure itself against that liability, which does not impede recovery by the person injured:
Given that UBS’s liability for gross negligence could be passed on to an insurer, there would appear to be no reason not to permit an insurer to absorb such liability by waiving a right of subrogation for such conduct.
St. Paul points out that a party is not permitted to deprive compensation to those injured by its gross negligence by the device of inserting into a contract a clause exculpating the party from liability for its own gross negligence... This rule, however, simply ensures that a párty injured by another’s gross negligence will be able to recover its losses. To an injured party, it is irrelevant whether it recovers from the grossly negligent party or from an insurer. This rule, thus, does not bear on the lawfulness of a clause affecting an insurer’s right to recover from a party who was grossly negligent.
Id. at 341 (emphasis in original).
The court noted the existence of other district court decisions that had held sub-rogation waivers unenforceable in the face of claims of gross negligence; but it disagreed with those decisions because they
failed to distinguish between the public policy behind insuring that a victim is paid, and a competing policy permitting parties to avoid costly litigation over whether a party was, or was not, grossly negligent, through the use of insurance (and waivers of subrogation).
Id. at 342.
Concluding that the waiver-of-subrogation clause was valid and enforceable, the district court granted the motions to dismiss plaintiffs’ complaint.
The court also granted the motions of TIG, AIU, and Royal to dismiss UBS’s third-party complaint, ruling that the'policies issued to UBS by those insurers were designed to avoid overlap with the builder’s risk policy, see id. at 343, and “cannot be interpreted to require them to defend UBS in this action, or to include coverage for the losses reimbursed to Durst and FTSA by St. Paul pursuant to the Policy,” id. at 342. The court denied all other pending motions as moot, and ordered that judgment be entered closing the case.
D. The Issues on This Appeal
Plaintiffs filed a timely notice of appeal, challenging the district court’s judgment [80]*80“granting all motions to dismiss plaintiffs’ Complaint and defendant Universal Builders' Supply Inc.’s Third-Party Complaint.” (Plaintiffs’ Notice of Appeal dated April 19, 2004, at 1.) They principally pursue their contentions that the waiver-of-subrogation clause in the St. Paul Policy is unenforceable on the theory that UBS breached its obligation under the Construction Contract to obtain waivers of subrogation by TIG, AIU, and Royal, and that as against a claim of gross negligence, waivers of sub-rogation are unenforceable as a matter of public policy. Plaintiffs also argue that the district court erred in concluding that the policies issued by TIG, AIU, and Royal do not require those insurers to defend and indemnify UBS with respect to plaintiffs’ claims in the present action.
Before addressing the merits of these arguments, we note that the third-party defendants raise two substantial procedural matters. First, they contend that to the extent that recovery is sought on behalf of Durst and FTSA, the district court lacked subject matter jurisdiction because there is no diversity of citizenship; they urge, however, that if we agree that diversity is lacking, we should drop the nondiverse parties from the suit rather than ordering that the entire action be dismissed for lack of jurisdiction. Second, the third-party defendants contend that, in any event, plaintiffs lack standing to challenge the dismissal of UBS’s third-party complaint.
For the reasons that follow, we conclude that diversity of citizenship is lacking but that the nondiverse plaintiffs should be dropped in order to cure that defect and permit resolution of this action between St. Paul and UBS; and we conclude that St. Paul lacks standing to challenge the dismissal of UBS’s third-party complaint. As to the merits, we conclude that the district court properly dismissed the complaint against UBS.
II. THE JURISDICTIONAL ISSUES
A. Diversity Jurisdiction
To the extent pertinent to this case, the district courts have diversity jurisdiction where, assuming the requisite amount in controversy, the suit is between “citizens of different States,” 28 U.S.C. § 1332(a)(1). It is well established that for a case to fit within this section, there must be “complete” diversity. Owen Equipment & Erection Co. v. Kroger, 437 U.S. 365, 373, 98 S.Ct. 2396, 57 L.Ed.2d 274 (1978); see, e.g., Strawbridge v. Curtiss, 7 U.S. (3 Crunch) 267, 267, 2 L.Ed. 435 (1806). Diversity is not complete if any plaintiff is a citizen of the same state as any defendant. See, e.g., id.; Owen Equipment & Erection Co. v. Kroger, 437 U.S. at 373-74, 98 S.Ct. 2396.
In this respect, it has long been “established that the ‘citizens’ upon whose diversity a plaintiff grounds jurisdiction must be real and substantial parties to the controversy.” Navarro Savings Ass’n v. Lee, 446 U.S. 458, 460, 100 S.Ct. 1779, 64 L.Ed.2d 425 (1980) (“Navarro”); see, e.g., Coal Co. v. Blatchford, 78 U.S. (11 Wall.) 172, 177, 20 L.Ed. 179 (1870); Marshall v. Baltimore & Ohio Railroad Co., 57 U.S. (16 How.) 314, 328-29, 14 L.Ed. 953 (1853); McNutt v. Bland, 43 U.S. (2 How.) 9, 15, 11 L.Ed. 159 (1844). Thus, “a federal court must disregard nominal or formal parties and rest jurisdiction only upon the citizenship of real parties to the controversy.” Navarro, 446 U.S. at 461, 100 S.Ct. 1779. It is also well established that when the question is subject matter jurisdiction, the court is permitted to rely on information beyond the face of the complaint. See, e.g., United Food & Commercial Workers Union, Local 919 v. CenterMark Properties Meriden Square, Inc., 30 F.3d 298, 305 (2d Cir.1994); Metro Industrial [81]*81Painting Corp. v. Terminal Construction Co., 287 F.2d 382, 384 (2d Cir.1961); 5B C. Wright & A. Miller, Federal Practice and Procedure § 1350, at 160 (3d ed.2004).
Where a plaintiff sues “as subrogee” of another named plaintiff, there may be a question as to whether the subrogee is the only plaintiff that is a real party to the controversy or whether the subrogor is a real party as well, rather than merely a nominal or formal party. In discussing a diversity issue in Navarro, which did not involve subrogation, the Supreme Court noted that, although Fed.R.Civ.P. 17(a) (“[e]very action shall be prosecuted in the name of the real party in interest”) and § 1332 serve different purposes, and may warrant different outcomes, “[t]here is a ‘rough symmetry’ between the ‘real party in interest’ standard of Rule 17(a) and the rule that diversity jurisdiction depends upon the citizenship of real parties to the controversy.” Navarro, 446 U.S. at 462 n. 9, 100 S.Ct. 1779. In United States v. Aetna Casualty & Surety Co., 338 U.S. 366, 70 S.Ct. 207, 94 L.Ed. 171 (1949) (“Aetna”), the Supreme Court, discussing the requirements of Rule 17(a) in the context of subrogation, drew the following line:
If the subrogee has paid an entire loss suffered by the insured, it is the only real party in interest .... If it has paid only part of the loss, both the insured and insurer (and other insurers, if any, who have also paid portions of the loss) have substantive rights against the tort-feasor which qualify them as real parties in interest.
338 U.S. at 380-81, 70 S.Ct. 207. See also Ocean Ships, Inc. v. Stiles, 315 F.3d 111, 116-17 (2d Cir.2002) (insured plaintiff that had not been reimbursed for its $5,000 deductible was a real party in interest within the meaning of Rule 17(a)).
Even where the insurer has paid only part of the insured’s loss, however, giving both insurer and insured real stakes in the outcome, “[t]hey are clearly not ‘indispensable’ parties” within the meaning of Fed.R.Civ.P. 19. Aetna, 338 U.S. at 382 & n. 19, 70 S.Ct. 207 (discussing original Rule 19); see also Provident Tradesmens Bank & Trust Co. v. Patterson, 390 U.S. 102, 117 n. 12, 88 S.Ct. 733, 19 L.Ed.2d 936 (1968) (1966 amendment to Rule 19 cured “ ‘defective ... phrasing’ ” and did not alter its underlying principles (quoting Fed. R.Civ.P. 19 Advisory Committee Note (1966))). Thus, where the insurer has not fully compensated the insured for its loss, “either party may sue” without the presence of the other. Aetna, 338 U.S. at 381, 70 S.Ct. 207. In such a case, if joinder of the absent insured or insurer would deprive the court of jurisdiction over the subject matter of the action, the court may properly proceed in accordance with Rule 19 to adjudicate the rights of the suing plaintiff alone; the consequence is that the defendant “may have to defend two or more actions on the same tort.” Aetna, 338 U.S. at 382, 70 S.Ct. 207.
By the same token, the courts have the power, “on such terms as are just,” Fed.R.Civ.P. 21, “to allow a dispensable nondiverse party to be dropped at any time, even after judgment has been rendered,” Newman-Green, Inc. v. Alfonzo-Larrain, 490 U.S. 826, 832, 109 S.Ct. 2218, 104 L.Ed.2d 893 (1989) ("Newman-Green”).
“[T]he question always is, or should be, when objection is taken to the jurisdiction of the court by reason of the citizenship of some of the parties, whether ... they are indispensable parties, for if their interests are severable and a decree without prejudice to their rights can be made, the jurisdiction of the [82]*82court should be retained and the suit dismissed as to them.”
Id. at 835, 109 S.Ct. 2218 (quoting Horn v. Lockhart, 84 U.S. (17 Wall.) 570, 579, 21 L.Ed. 657 (1873)). Further, and of significance to this appeal, “[although the Federal Rules of Civil Procedure strictly apply only in the district courts, ... the policies informing Rule 21 may apply equally to the courts of appeals.” Newman-Green, 490 U.S. at 832, 109 S.Ct. 2218. Thus, “a court of appeals may [itself] ... dismiss a dispensable nondiverse party” without remanding to the district court for that action. Id.; see id. at 837, 109 S.Ct. 2218.
In sum, in a diversity case in which both the insurer as subrogee and the insured are plaintiffs and the insurer has paid only part of the loss incurred by the insured, if the presence of either the insurer or the insured destroys diversity, both the district court and the court of appeals have the authority even after the entry of judgment, absent prejudice to any party, to drop the nondiverse party— whether insurer or insured — in order to preserve subject matter jurisdiction.
In the present case, the complaint asserted that jurisdiction was premised on diversity of citizenship. The complaint alleged, however, that Durst is a New York corporation and that FTSA is a New York limited liability company; and it alleged, and UBS admitted in its answer, that UBS is a New York corporation. Thus, plaintiffs Durst and FTSA and defendant UBS are citizens of New York. Although the complaint styles St. Paul as suing as sub-rogee of FTSA and Durst and frequently refers to “plaintiff’ in the singular, it is clear that Durst and FTSA are interested parties, in both form and substance. As a matter of form, Durst and FTSA are denominated among the “Plaintiffs” in, inter alia, the caption and first paragraph of the complaint, the notice of appeal, and the brief of “Plaintiffs-Appellants” on this appeal. As a matter of substance, plaintiffs acknowledge that “St. Paul ... reimbursed Four Times Square ... and Durst approximately $19 million of their $20 million in losses. Thus, as subrogee, St. Paul’s claim is for approximately $19 million, plus interest. Four Times Square and Durst’s claim against UBS is for about $1 million.” (Plaintiffs’ brief on appeal at 16-17 (emphases added).) “The ad damnum clause in the complaint seeks $20 million in damages; i.e., $19 million for St. Paul’s damages as subrogee, and $1 million for Durst and Four Times Square’s damages.” {Id. at 17 n. 6. (emphases added).)
It is thus clear that Durst and FTSA, which would recover $1 million if the complaint in this action were upheld, are parties having a real stake in this controversy. Given that they and UBS are citizens of New York, the presence of Durst and FTSA destroys diversity.
The third-party defendants persuasively urge us to exercise our authority under Fed.R.Civ.P. 21 to drop the nondiverse plaintiffs rather than ordering that the entire action, which has been pending for some five years, be dismissed for lack of jurisdiction. In the interest of judicial efficiency, and in the absence of any indication that dropping Durst and FTSA will cause any party prejudice, we hereby dismiss Durst and FTSA from the action, leaving St. Paul as the only plaintiff.
B. Standing To Appeal Dismissal of the Third-Party Complaint
The third-party defendants contend also that St. Paul lacks standing to appeal from so much of the district court’s decision as dismissed UBS’s third-party complaint against them. We agree.
[83]*83“Ordinarily, only a party aggrieved by a judgment or order of a district court may exercise the statutory right to appeal therefrom.” Deposit Guaranty National Bank v. Roper, 445 U.S. 326, 333, 100 S.Ct. 1166, 63 L.Ed.2d 427 (1980). “Federal appellate jurisdiction is limited by the appellant’s personal stake in the appeal.” Id. at 336, 100 S.Ct. 1166. A party ordinarily has no standing to appeal from part of a judgment that dismisses a claim to which it was not a party. See, e.g., Bryant v. Technical Research Co., 654 F.2d 1337, 1343 (9th Cir.1981) (dismissing for lack of standing the defendant’s appeal from so much of the judgment as dismissed two third-party defendants against which the defendant had not asserted a claim); see also St. Pierre v. Dyer, 208 F.3d 394, 399 (2d Cir.2000) (where third-party defendant had not been sued by the plaintiff, it had “no status as a party to [the plaintiffs] appeal”).
In the present case, UBS’s third-party complaint asserted that TIG, AIU, and Royal were obligated to defend UBS with respect to claims asserted against it by St. Paul and to indemnify it if St. Paul prevailed. Although St. Paul seeks to challenge the dismissal of those claims, St. Paul was not a party to those claims. Application of the above principles leads to the conclusion that St. Paul lacks standing to challenge the dismissal of the third-party complaint.
St. Paul argues that it should be allowed to appeal the dismissal of the third-party claims because it has an interest in seeing that any judgment it wins against UBS will be collectible. However, under New York law, St. Paul does not have an interest sufficient to allow it to assert claims directly against TIG, AIU, or Royal as insurers of UBS unless St. Paul first obtains a judgment against UBS. See, e.g., Lang v. Hanover Insurance Co., 3 N.Y.3d 350, 352, 787 N.Y.S.2d 211, 212, 820 N.E.2d 855 (2004) (“a judgment” against the tortfeasor “is a statutory condition precedent to a direct suit against the tort-feasor’s insurer”); id. at 355, 787 N.Y.S.2d at 214, 820 N.E.2d 855 (until it obtains a judgment against the tortfeasor, an injured party lacks “standing to sue a tort-feasor’s insurer”). Given St. Paul’s lack of standing to sue the third-party defendants directly, we surely see no reason to depart from the general principle that one lacks standing to challenge a judgment adjudicating a claim to which it was not a .party.
In any event, given our conclusion in Part III below that St. Paul’s claims were properly dismissed, any interest St. Paul may have had in the collectibility of a judgment upholding those claims is moot.
III. THE MERITS
A. The Breach-of-Contract Theory
In support of its contention that the waiver-of-subrogation clause is unenforceable by reason of a breach of contract by UBS, St. Paul relies on the Insurance Rider’s “Subrogation and Waiver” clause stating that the “Owner ... waive[s] all rights ... against separate Contractors ... for damages caused by fire or other perils to the extent covered by insurance obtained pursuant to Owner’s ‘All Risk’ Builder’s Risk Insurance or any other property insurance applicable to the Work” (Rider § II.8), that the “Owner ... shall require of ... Contractors ... similar waivers, each in favor of all other parties enumerated above” (id.), and that “[a]ll certificates of insurance shall indicate, in the special items section, that waiver of subrogation has been endorsed to the insurance policies” (id.). St. Paul argues that “th[is] clause requires that each party waive subrogation • rights as against the other, and require their insurers to do the same” (Plaintiffs’ brief on [84]*84appeal at 13), that the TIG, AIU, and Royal, policies covering UBS “contain clauses barring [UBS] from waiving its [sic] subrogation rights” (id. at 25), and that UBS thereby breached its obligation to waive subrogation, making St. Paul’s waiver unenforceable. This contention suffers both legal and factual flaws.
Subrogation is an “equitable doctrine [that] allows an insurer to stand in the shoes of its insured and seek indemnification from third parties whose wrongdoing has caused a loss for which the insurer is bound to reimburse.” Kaf-Kaf, Inc. v. Rodless Decorations, Inc., 90 N.Y.2d 654, 660, 665 N.Y.S.2d 47, 49, 687 N.E.2d 1330 (1997). The “parties to an agreement may waive their insurer’s right of subrogation.” Id. at 660, 665 N.Y.S.2d at 49-50, 687 N.E.2d 1330. However, “a waiver of subrogation clause cannot be enforced beyond the scope of the specific context in which it appears .... ” Id. at 660, 665 N.Y.S.2d at 50, 687 N.E.2d 1330; see, e.g., S.S.D.W. Co. v. Brisk Waterproofing Co., 76 N.Y.2d 228, 236, 557 N.Y.S.2d 290, 294-95, 556 N.E.2d 1097 (1990). By the same token, an obligation to secure a waiver-of-subrogation clause does not'exist with respect to a type of insurance not encompassed by the contractual obligation to obtain such a waiver.
New York law recognizes a distinction between property insurance and liability insurance. See, e.g., Tokio Marine & Fire Insurance Co. v. Employers Insurance of Wausau, 786 F.2d 101, 104 (2d Cir.1986) (“Tokio ”); Board of Education v. Valden Associates, Inc., 46 N.Y.2d 653, 657, 416 N.Y.S.2d 202, 203, 389 N.E.2d 798 (1979) (“Valden ”). A builder’s risk policy is a form of property insurance that covers the interests of the owner, contractor, subcontractors, and others involved in the construction project, insuring them against risks of property damage to the project. See, e.g., Tokio, 786 F.2d at 104. Contract provisions that require the procurement of such a policy and require the owner, contractor, and all other involved parties to waive all rights against each other for damages caused by perils covered by that insurance “in effect simply require one of the parties to the contract to provide insurance for all of the parties.” Valden, 46 N.Y.2d at 657, 416 N.Y.S.2d at 203, 389 N.E.2d 798. In connection with such a policy, “[a] waiver of subrogation is useful ... because it avoids disruption and disputes among the parties to the projéct. It thus eliminates the need for lawsuits, and yet protects the contracting parties from loss by bringing all property damage under the all risks builder’s property insurance.” Tokio, 786 F.2d at 104; see, e.g., 4 P. Bruner & P. O’Connor, Construction Law § 11:100 (2002) (“Construction contracts often contain provisions which require the parties to waive their right to claim damages against one another up to the amount of insurance coverage available for their losses. These ‘waiver of subrogation’ provisions are intended to cut down the amount of litigation that might otherwise arise due to the existence of an insured loss.”). Such waivers are commonplace. See, e.g., Tokio, 786 F.2d at 104 (describing waiver-of-subrogation clause as “standard”); S. Turner, Insurance Coverage, of Construction Disputes § 5:7 (2004) (“waivers of subrogation are quite common in construction contracts as to the subro-gation rights of property insurance insurers.... and case law has upheld these waivers, against ... the subrogated insurer”).
A liability insurance policy is different in kind from a builder’s risk policy covering damage to the construction project. A liability policy covers “damage to third parties ... such as injuries to passersby or damage to adjoining proper[85]*85ty.” Tokio, 786 F.2d at 104. “[T]hird-party liability insurance ... is not similar to ... first-party property coverage[ ]”; each “encompasses a different classification of risks and, by extension, each protects against exposure to different liabilities,” with the latter covering damage to “property” or “assets” of the insured, and the former covering “injury ... to [a third-party] himself.” Great Northern Insurance Co. v. Mount Vernon Fire Insurance Co., 92 N.Y.2d 682, 689, 685 N.Y.S.2d 411, 415, 708 N.E.2d 167 (1999).
In the present case, the “Subrogation and Waiver” clause of the Insurance Rider relied on by St. Paul, i.e., Rider § U.8., deals with the contractual ramifications of builder’s risk insurance. As indicated by the language quoted at the beginning of this Part, that clause requires mutual waivers by the Owner and contractors of their rights to recover against each other only “to the extent covered by insurance obtained pursuant to Owner’s ‘All Risk’ Builder’s Risk Insurance or any other property insurance applicable to . the Work.” (Rider § II.8. (emphases added).) The subrogation and waiver clause does not purport to deal with liability insurance.
The policies issued to UBS by AIU and Royal were for, respectively, commercial general “LIABILITY” insurance and excess “LIABILITY” insurance. Similarly, the TIG insurance policy obtained by the Owner, which covered UBS, was an excess “LIABILITY” policy. The Insurance Rider imposed no obligation on UBS to obtain any waiver of subrogation in liability policies.
Further, St. Paul’s contention that AIU Policy § IV.8., Royal Policy § VIII.12., and TIG Policy § IV.N. “explicitly prohibit ]” UBS from waiving subrogation rights (Plaintiffs’ brief on appeal at 14, 15) is not supported by the language of those policies. As quoted in Part I.A. above, those sections did not prohibit UBS from impairing the insurers’ subrogation rights excépt “after loss.”
In sum, UBS’s acceptance of the provisions in the TIG, AIU, and Royal policies did not breach UBS’s obligations under the Insurance Rider or the Construction Contract. The district court properly rejected St. Paul’s contention that the waiver-of-subrogation clause was unenforceable by reason of UBS’s alleged breach of contract.
B. The Public Policy Theory
Finally, St. Paul contends that even if UBS breached no contractual obligation, a waiver-of-subrogation clause is unenforceable where the claim is that the loss resulted from the defendant’s gross negligence. Although the New York Court , of Appeals has not addressed this precise question, we agree with the district court that, based on the pertinent well-established principles of New York law, St. Paul’s contention should be rejected.
The principle to which St. Paul would have us analogize is that New York “[p]ublic policy ... forbids a party’s attempt to escape liability, through a contractual clause, for damages occasioned by grossly negligent conduct.” Colnaghi, U.S.A., Ltd. v. Jewelers Protection Services, Ltd., 81 N.Y.2d 821, 823, 595 N.Y.S.2d 381, 382-83, 611 N.E.2d 282 (1993) (internal quotation marks omitted). This prohibition applies to- bar so-called “exculpatory clauses,” which “typically deprive a contracting party of the right to recover for damages suffered as the result of the exonerated party’s tortious act,” Austro v. Niagara Mohawk Power Corp., 66 N.Y.2d 674, 676, 496 N.Y.S.2d 410, 410, 487 N.E.2d 267 (1985). Thus, “[t]o the extent that agreements purport to grant exemption for liability for willful or grossly [86]*86negligent acts they have been viewed as wholly void.” Gross v. Sweet, 49 N.Y.2d 102, 106, 424 N.Y.S.2d 365, 367, 400 N.E.2d 306 (1979).
It is important, however, to “distinguish between [such] exculpatory clauses” and “indemnity contracts that simply shift the source of compensation without restricting the injured party’s ability to recover.” Austro v. Niagara Mohawk Power Corp., 66 N.Y.2d at 676, 496 N.Y.S.2d at 410, 487 N.E.2d 267 (emphasis added). The latter agreements are not contrary to public policy unless they purport to indemnify a party for damages flowing from an injury that was intentional. See id. The New York Court of Appeals has held that a party may obtain insurance as protection against its own gross negligence. See, e.g., Public Service Mutual Insurance Co. v. Goldfarb, 53 N.Y.2d 392, 400, 442 N.Y.S.2d 422, 427, 425 N.E.2d 810 (1981) (“indemnity for compensatory damages would be allowable” for acts of “gross negligence, recklessness or wantonness”); Town of Massena v. Healthcare Underwriters Mutual Insurance Co., 98 N.Y.2d 435, 445, 749 N.Y.S.2d 456, 460-61, 779 N.E.2d 167 (2002) (although insurance coverage for intentional injuries cannot “[a]s a matter of policy ... [be] covered by insurance,” insurance coverage for “reckless” conduct “would not be precluded by public policy” (emphasis omitted)).
The decision of the New York Court of Appeals in Valden highlighted the distinction between exculpatory clauses and indemnity agreements in connection with builder’s risk policies. The construction contract in Valden “required the owner to provide ‘fire, extended coverage, vandalism and malicious mischief insurance upon the entire structure on which the work of the Contract [wa]s to be done,’” and “also provided that ‘[t]he Owner, Contractor, and all subcontractors waive all rights, each against the others, for damages caused by fire or other perils covered by insurance provided for under the terms of the Contract Documents, except such rights as they may have to the proceeds of insurance.’ ” 46 N.Y.2d at 655-56, 416 N.Y.S.2d at 202-03, 389 N.E.2d 798. The requisite builder’s risk insurance was obtained; a fire caused damage to the property; and the insurer paid the loss claim filed by the owner and then, as subrogee of the owner, attempted to obtain reimbursement from the contractor and subcontractors whose negligence allegedly caused the fire. The defendants argued that the contractual waivers quoted above barred suit against them by the insurer. The insurer contended that the waivers were barred by a statutory provision that states that agreements in which a contractor purports to “exemptf ] himself from liability for injuries to person or property caused by or resulting from the negligence of such contractor ... shall be deemed to be void as against public policy and wholly unenforceable,” N.Y. Gen. Oblig. Law § 5-323 (McKinney 2001). The Valden Court rejected the insurer’s contention, stating that “[a] distinction must be drawn between contractual provisions which seek to exempt a party from liability to persons who have been injured or whose property has been damaged,” and “contractual provisions, such as those involved in this suit, which in effect simply require one of the parties to the contract to provide insurance for all of the parties” involved in the construction project, Valden 46 N.Y.2d at 657, 416 N.Y.S.2d at 203, 389 N.E.2d 798 (emphases added), and thereby shift to an insurance company the risk of damage to the construction property. “Absent any indication of overreaching or unconscionability,” the latter type of provision “violate[s] neither section 5-323 of the General Obli[87]*87gations Law nor any other public policy. Id. (emphasis added).
Although St. Paul seeks to distinguish Valden on the ground that it dealt with a claim of simple, not gross, negligence, we conclude that that difference is immaterial given the other New York cases referred to above, establishing that insurance coverage for gross negligence is not contrary to public policy.
CONCLUSION
We have considered all of St. Paul’s contentions that are properly before us and have found them to be without merit. For the reasons stated above, to the extent that the appeal challenges the district court’s dismissal of the third-party complaint, the appeal is dismissed for lack of standing. The judgment of the district court is modified pursuant to Fed.R.Civ.P. 21 to dismiss Durst and FTSA from the action, without prejudice; and as modified, the judgment dismissing the complaint is affirmed.