*156Appellant-Cross-Appellee Reed Smith LLP ("Reed Smith") appeals an order from the district court (Naomi R. Buchwald, J. ) enjoining its action for tortious interference and unjust enrichment in New York state court against Wohl & Fruchter LLP ("Wohl & Fruchter"), which dispute arose from the two firms' concurrent representation of the plaintiff class in the now-settled litigation Kaplan v. S.A.C. Capital Advisors, L.P. , No. 12-Civ.-9350 (S.D.N.Y.). The district court concluded, inter alia, that its decision during settlement proceedings that the fees that Wohl & Fruchter received were "fair and reasonable" decided an element of Reed Smith's tortious interference and unjust enrichment claims by resolving that Wohl & Fruchter had not "pocketed, at Reed Smith's expense, more fees than the amount to which it was entitled." Kaplan v. S.A.C. Capital Advisors, L.P. , No. 12-Civ.-9350, 2017 WL 6403087, at *10 (S.D.N.Y. Nov. 16, 2017). We affirm.

BACKGROUND

Wohl & Fruchter served as co-class counsel in Kaplan v. S.A.C. Capital Advisors, L.P. , No. 12-cv-9350, a securities class action filed in December 2012 in the Southern District of New York. By June 2016, the class action was headed for trial, and Wohl & Fruchter sought and engaged trial counsel to assist in its representation of the class. Wohl & Fruchter recommended and the class's lead plaintiffs ("Lead Plaintiffs") originally engaged Quinn Emanuel Urquhart & Sullivan LLP ("Quinn Emanuel") as trial counsel. In September, however, less than four months before trial was scheduled to begin, Quinn Emanuel withdrew due to an alleged conflict of interest. In Quinn Emanuel's stead, Wohl & Fruchter recommended and the Lead Plaintiffs engaged Reed Smith on September 19, 2016. Wohl & Fruchter notified defense counsel of Reed Smith's engagement that day, and at a hearing on September 21, defense counsel alerted the court that Reed Smith might be conflicted. The next day, the class action defendants contacted class counsel (specifically, Wohl & Fruchter) about restarting settlement negotiations. On September 23, after obtaining Lead Plaintiffs' authorization to terminate Reed Smith's engagement, class counsel notified Reed Smith that the firm was terminated. Wohl & Fruchter did not involve Reed Smith in settlement negotiations.

The parties to the securities class action reached a settlement in late November, and the district court preliminarily approved the settlement on December 16, 2016. The district court's preliminary approval order called for any counsel that believed it was entitled to fees or expenses from the litigation to make an application to the court. Despite having notice of this order, Reed Smith did not make such an application.

*157The district court formally approved the settlement in May of 2017 and approved a fee and expense award to Wohl & Fruchter and an expense award to Quinn Emanuel (the "Fee Order"). The settlement approval order also instructed that "[e]xcept as approved hereby or by other Order of this Court, no person shall be entitled to attorneys' fees for the reimbursement of litigation expenses in connection with the representation of the Elan Class Plaintiffs or the Classes in this Action." Final Judgment & Order of Dismissal with Prejudice at 5, ¶ 8, Kaplan v. S.A.C. Capital Advisors, L.P. , No. 1:12-cv-9350 (JGK) (KNF) (S.D.N.Y. May 12, 2017), ECF No. 391. The district court retained exclusive jurisdiction to decide "any further applications for attorneys' fees or requests for reimbursement of litigation expenses in connection with the representation of the Elan Class Plaintiffs or the Classes in this Action, and over all parties to the Action in connection therewith." Id. at 5, ¶ 10.

About one month after the district court approved the settlement, Reed Smith filed a complaint against Wohl & Fruchter in the New York Supreme Court that alleged claims arising from the firms' co-representation of the class. Specifically, the complaint alleged that Wohl & Fruchter had tortiously interfered with Reed Smith's engagement contract with the Lead Plaintiffs and that Wohl & Fruchter had been unjustly enriched by its unlawful behavior in doing so. The complaint sought damages of $ 6,750,000, the amount Reed Smith allegedly would have been entitled to under the engagement agreement had it remained in force. On July 28, 2017, Wohl & Fruchter filed a motion in the District Court for the Southern District of New York requesting that the district court permanently enjoin the state-court proceedings and dismiss Reed Smith's state claims on the merits. The district court granted the motion to the extent it sought an injunction barring Reed Smith from pursuing the state-court proceeding but declined to make any ruling on the merits of Reed Smith's tortious interference and unjust enrichment claims.

DISCUSSION

I. The District Court Had Ancillary Jurisdiction over the Motion to Stay

Reed Smith argues that the district court did not have jurisdiction to decide Wohl & Fruchter's motion to stay the state-court proceedings. We review the district court's decision on subject matter jurisdiction for clear error as to factual findings and de novo as to its legal conclusions. Lyndonville Sav. Bank & Tr. Co. v. Lussier , 211 F.3d 697, 701 (2d Cir. 2000).

Where a district court has original jurisdiction over a civil action, "it retains ancillary jurisdiction after dismissal to adjudicate collateral matters such as attorney's fees." In re Austrian & German Bank Holocaust Litig. , 317 F.3d 91, 98 (2d Cir. 2003). This grant of ancillary jurisdiction empowers the district court to "take actions necessary 'to manage its proceedings, vindicate its authority, and effectuate its decrees.' " Hendrickson v. United States , 791 F.3d 354, 358 (2d Cir. 2015) (quoting Kokkonen v. Guardian Life Ins. of Am. , 511 U.S. 375, 380, 114 S.Ct. 1673, 128 L.Ed.2d 391 (1994) ). In Kokkonen , the Supreme Court concluded that ancillary jurisdiction arises where "the parties' obligation to comply with the terms of the settlement agreement ha[s] been made part of the order of dismissal-either by separate provision (such as a provision 'retaining jurisdiction' over the settlement agreement) or by incorporating the terms of the settlement agreement in the order." Kokkonen , 511 U.S. at 381, 114 S.Ct. 1673.

*158The district court, construing its ancillary jurisdiction as supplemental jurisdiction, properly exercised jurisdiction over Wohl & Fruchter's motion to stay the state-court proceedings because the motion implicates the district court's ability to effectuate its decrees. In its motion to stay, Wohl & Fruchter claims that Reed Smith is attempting to circumvent the district court's Fee Order by bringing its claims in state court. In other words, Wohl & Fruchter's motion raises an issue regarding the continued integrity of the district court's decision on attorneys' fees. Thus, in deciding the motion to stay, the district court exercised its power to effectuate its decrees, and therefore the district court had ancillary jurisdiction over the motion to stay.

II. The District Court Properly Declined to Abstain from Exercising Jurisdiction

Reed Smith next argues that even if the district court had jurisdiction over Wohl & Fruchter's motion, it should have abstained from exercising its jurisdiction. We disagree. A district court should abstain from deciding cases over which it has jurisdiction "only in the exceptional circumstances where the order to the parties to repair to the state court would clearly serve an important countervailing interest." Colo. River Water Conservation Dist. v. United States , 424 U.S. 800, 813, 96 S.Ct. 1236, 47 L.Ed.2d 483 (1976) (internal quotation marks omitted). To determine whether a district court should have abstained from exercising jurisdiction, we weigh six factors:

(1) whether the controversy involves a res over which one of the courts has assumed jurisdiction; (2) whether the federal forum is less inconvenient than the other for the parties; (3) whether staying or dismissing the federal action will avoid piecemeal litigation; (4) the order in which the actions were filed and whether proceedings have advanced more in one forum than in the other; (5) whether federal law provides the rule of decision; and (6) whether the state procedures are adequate to protect the plaintiff's federal rights.

Woodford v. Cmty. Action Agency of Greene Cty., Inc. , 239 F.3d 517, 522 (2d Cir. 2001) (citations omitted). "No single factor is necessarily decisive, and the weight to be given to any one factor may vary greatly from case to case, depending on the particular setting of the case." Vill. of Westfield v. Welch's , 170 F.3d 116, 121 (2d Cir. 1999) (citation omitted) (internal quotation marks omitted). Where a factor "is facially neutral, that is a basis for retaining jurisdiction, not for yielding it." Niagara Mohawk Power Corp. v. Hudson River-Black River Regulating Dist. , 673 F.3d 84, 101 (2d Cir. 2012) (internal quotation marks omitted).

The parties do not contest factors one or two, which we agree are neutral and thus favor the district court retaining jurisdiction. See id . As to factor three, there is no risk of inconsistent judgments. Woodford , 239 F.3d at 524 (construing the third factor as typically concerned with whether the federal lawsuit "pose[s] a risk of inconsistent outcomes not preventable by principles of res judicata and collateral estoppel"). Further, as to factors four and five, the federal court had jurisdiction over the underlying suit before the state court did, and federal law provides the rule of decision for this motion. As to factor six, "[w]e do not doubt that the New York courts provide a fair alternative forum" to vindicate Wohl & Fruchter's rights under the Fee Order, and this factor is at best for Reed Smith neutral. Niagara Mohawk , 673 F.3d at 103 ; see also Vill. of Westfield , 170 F.3d at 124 ("This factor is more important when it weighs in favor of federal *159jurisdiction." (internal quotation marks omitted)). Therefore, all six factors weigh in favor of retaining jurisdiction. The district court did not abuse its discretion in exercising its jurisdiction over the motion to stay.

III. The Injunction was Proper Under the Anti-Injunction Act

The Anti-Injunction Act limits a court's usually expansive power to issue writs, providing: "A court of the United States may not grant an injunction to stay proceedings in a State court except as expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments." 28 U.S.C. § 2283. The Act therefore provides three exceptions under which a district court may determine a stay is appropriate. As relevant here, we commonly refer to the second exception as the "in-aid-of-jurisdiction exception" and the third exception as the "relitigation exception." The district court enjoined Reed Smith's state-court action by concluding that an injunction was necessary in aid of the district court's jurisdiction and in order to prevent relitigation of issues the federal court had already decided. We conclude that the relitigation exception applies, and without needing to consider the in-aid-of-jurisdiction exception, we find that the district court therefore properly enjoined the state-court proceedings.

The relitigation exception "is designed to implement well-recognized concepts of claim and issue preclusion." Smith v. Bayer Corp. , 564 U.S. 299, 306, 131 S.Ct. 2368, 180 L.Ed.2d 341 (2011) (internal quotation marks omitted). For claim preclusion to apply, there must be a final judgment from one court that "forecloses successive litigation of the very same claim, whether or not relitigation of the claim raises the same issues as the earlier suit." Taylor v. Sturgell , 553 U.S. 880, 892, 128 S.Ct. 2161, 171 L.Ed.2d 155 (2008) (internal quotation marks omitted). For issue preclusion to apply, the same "issue of fact or law" must have been "actually litigated and resolved in a valid court determination essential to the prior judgment, even if the issue recurs in the context of a different claim." Id. (internal quotation marks omitted). The district court concluded that an injunction was necessary to prevent relitigation because Reed Smith's claims were barred by issue preclusion.

In Wyly v. Weiss , we held that issue preclusion could support an injunction where members of a class action brought a state-court action alleging that class counsel had committed legal malpractice. 697 F.3d 131, 144 (2d Cir. 2012). We concluded that the district court's decision that class counsel's fee award was fair and reasonable "resolved one of the elements of a malpractice claim-namely, counsel's deficient performance." Id. at 141. The dissatisfied class members' lawsuit was therefore "a collateral attack on the District Court's findings that the Settlement was fair, reasonable and adequate, that class counsel was entitled to an award of attorneys' fees, and that those fees were fair and reasonable." Id. at 142 (internal quotation marks omitted). An injunction was necessary to prevent the state court from relitigating the district court's conclusion that counsel's performance was not deficient.

It is clear that like the claims brought by the dissatisfied appellants in Wyly , Reed Smith's state-court action for tortious interference and unjust enrichment is an impermissible end run around the district court's binding Fee Order. Despite Reed Smith's representations to the contrary, Reed Smith is seeking a fee award in state court based on a provision in Reed Smith's engagement letter that calls for *160the firm to be compensated, inter alia, "for a share of any recovery obtained by the Class." App'x at A-443, ¶ 33. Indeed, Reed Smith's state-court complaint charges that by not "making an application for attorneys' fees or reimbursement of expenses on behalf of Reed Smith," Wohl & Fruchter was acting "in direct contravention of the terms [Wohl & Fruchter] knew Reed Smith's former clients agreed to when Wohl negotiated the Engagement Agreement." App'x at A-447-48, ¶ 52. In Reed Smith's own words, "Reed Smith continues to be entitled to its bargained-for contingent fee, based on the amount of the Settlement, under the terms of the Engagement Agreement." App'x at A-448, ¶ 52; see also App'x at A-449, ¶ 57 ("Therefore, pursuant to the formula in the Engagement Agreement, Reed Smith is entitled to at least $ 6,750,000.00 in fees alone."). Reed Smith attempts to style the state-court action as something other than a request for fees, but the allegations in the state-court complaint belie this sleight of hand.

As in Wyly , the district court's fee award necessarily resolved elements of Reed Smith's state-court tortious interference and unjust enrichment claims. First, for Reed Smith's tortious interference claim to succeed under New York law, Reed Smith must show "(1) the existence of a valid contract between the plaintiff and a third party, (2) the defendant's knowledge of that contract, (3) the defendant's intentional procurement of a third-party's breach of contract without justification, and (4) damages." Tri-Star Lighting Corp. v. Goldstein , 58 N.Y.S.3d 448, 453, 151 A.D.3d 1102 (2d Dep't 2017) (internal quotation marks omitted). To satisfy the damages element, Reed Smith pleads in the state-court action that it was entitled to 5% of the class recovery pursuant to its contract with Lead Plaintiffs. To enforce that contract, however, Reed Smith was obligated to submit its claim to the district court during settlement proceedings. Because the district court's Fee Order definitively determined the fees for class counsel, Reed Smith cannot be entitled to a fee award and thus has not suffered damages. An element of Reed Smith's tortious interference claim, damages, is thus identical to an issue that was raised, litigated, and actually decided by the district court's Fee Order.

Second, under New York law, Reed Smith must show that "(1) defendant was enriched (2) at plaintiff's expense, and (3) that it is against equity and good conscience to permit defendant to retain what is sought to be recovered." Clark v. Daby , 300 A.D.2d 732, 751 N.Y.S.2d 622, 623 (3d Dep't 2002) (alterations omitted) (internal quotation marks omitted). Reed Smith cannot prevail on the second element of its unjust enrichment claim-"at plaintiff's expense"-for the same reason that it cannot prevail on the damages element of its tortious interference claim. An element of Reed Smith's unjust enrichment claim, its entitlement to any part of the settlement proceeds, is identical to an issue that was raised, litigated, and actually decided by the district court's Fee Order, which determined the fees to which class counsel were entitled. The district court therefore properly issued an injunction to prevent Reed Smith from relitigating the terms of the Fee Order.

IV. Wohl & Fruchter's Cross-Appeal Is Procedurally Untenable

Wohl & Fruchter argues that the district court erred in declining to decide the merits of Reed Smith's state-court claims, arguing that we should apply claim and issue preclusion to deny Reed Smith's claims. We see no abuse of discretion in the district court's refusal to adjudicate *161the merits of a claim that has not been asserted before it.

CONCLUSION

For the foregoing reasons, we AFFIRM the district court's injunction of Reed Smith's state-court action.