SUMMARY ORDER

AFTER ARGUMENT AND UPON DUE CONSIDERATION, IT IS HEREBY ORDERED, ADJUDGED AND DECREED that the judgment of the District Court is hereby AFFIRMED.

Plaintiffs-appellants Arnold E. Green-berg and Jay H. Koppel appeal from various pre-and post-trial rulings and from a September 28, 2000 judgment for defendants following a jury trial, all entered in the United States District Court for the Southern District of New York (Harold Baer, Jr., Judge, and Robert L. Carter, Judge ).* We assume familiarity with the factual background and procedural history set forth in the two reported opinions of the District Court, Koppel v. 4987 Corp., Nos. 96 Civ. 7570, 97 Civ. 1754, 1999 WL 608788 (S.D.N.Y. Aug.ll, 1999) and Koppel v. 4987 Corp., Nos. 96 Civ. 7570, 97 Civ. 1754, 2001 WL 47000 (S.D.N.Y. Jan.19, 2001), as well as our decision on a prior appeal in this case, Koppel v. 4987 Corp., 167 F.3d 125 (2d Cir. 1999).

On this appeal, plaintiffs claim that the District Court erred in its instructions to the jury on plaintiffs’ claims for breach of fiduciary duty and for violation of provisions of the Securities and Exchange Commission’s “anti-bundling” rule, 17 C.F.R. §§ 240.14a-4(a)(3), (b)(1). However, we need not reach the merits of these arguments. Any error in the instructions was harmless, because plaintiffs failed to present evidence sufficient to establish causation. See, e.g., LNC Invs., Inc. v. First Fidelity Bank, N.A., 173 F.3d 454, *636465 (2d Cir. 1999) (breach of fiduciary duty). Specifically, the record demonstrates that there was no viable alternative to the sale program that ultimately was adopted. Uncontradicted testimony and documentary evidence show that individuals or entities with effective veto power over alternative approaches made it impossible to pursue those options. For example, Leona Helmsley, acting on behalf of her husband’s ownership interest in the lessee of the property, refused to consent to the surrender of the lease and controlled a stake in the lessee sufficiently large for her to exercise veto power over any such proposal. Apple Bank, the mortgagee, was only conditionally willing to advance funds to pay the upcoming property tax assessment on the building. The Bank refused to lend the funds directly to the lessor, Garment Capitol Associates, despite defendant Peter Malkin’s offer of a personal guarantee for the loan. The Bank agreed to advance the necessary funds to the lessee, but it required personal guarantees from all four principals of the lessee—and those principals conditioned their guarantees on approval of all elements of the sale program that eventually was adopted, including the division of sale proceeds between lessor and lessee. In sum, the trial record is virtually devoid of evidence that defendants’ actions caused harm to plaintiffs; to the contrary, the record amply demonstrates that the sale program engineered by defendants was the only realistic mechanism for salvaging a seriously troubled investment. Any error in the District Court’s jury instructions, therefore, was harmless.

Plaintiffs also challenge the District Court’s post-trial ruling against them on their equitable claim for unjust enrichment. While not set forth as a separate argument, a corresponding challenge appears to be made to the sufficiency of the evidence supporting the jury verdict on the other claims. If these arguments are construed as challenges to the weight of the evidence supporting the District Court’s findings and/or the jury verdict, we lack appellate jurisdiction. De Falco v. Bernas, 244 F.3d 286, 325 (2d Cir.) (citing Stonewall Ins. Co. v. Asbestos Claims Mgmt. Corp., 73 F.3d 1178, 1199 (2d Cir. 1995), modified on other grounds, 85 F.3d 49 (2d Cir. 1996)), cert. denied sub nom. Dirie v. De Falco, — U.S. -, 122 S.Ct. 207, 151 L.Ed.2d 147 (2001). If, on the other hand, the arguments are viewed as challenges to the legal sufficiency of the evidence, we review for abuse of discretion and we need merely find that there was sufficient evidence from which the jury could have reached its verdict (or, in the case of the unjust enrichment claim, from which the District Court could have reached its conclusion). Id. at 325-26. Based on our review of the trial record, we conclude that this threshold has been met.

The District Court’s dismissal of plaintiffs’ fraud claims does not constitute reversible error. In August 1999, the District Court dismissed Koppel’s fraud claim for the first time, and we agree with the reasoning set forth in the District Court’s opinion. Koppel v. 4987 Corp., 1999 WL at *3-4. One year later, shortly before trial, the District Court requested a consolidated complaint, encompassing all surviving claims from the separate complaints of Koppel and Greenberg. Plaintiffs submitted a consolidated complaint that added back Koppel’s previously-dismissed fraud claim. The District Court’s request for a consolidated complaint, though, was not an invitation to ignore its prior rulings. The District Court properly enforced its request by excising Koppel’s previously-dismissed fraud claim from the consolidated complaint.

*637We also find no error in the District Court’s removal of Greenberg’s fraud claim from the consolidated complaint. Greenberg’s original complaint did not contain a claim for fraud (although, as discussed below, his complaint did contain a separate claim for “fraudulent scheme”). In the consolidated complaint submitted on the eve of trial, Greenberg added, for the first time, a claim for fraud. This claim was added to the complaint more than eight months after the close of discovery, without a motion to amend or any grant of permission from the District Court, and without even the requisite pleading of reliance. Under the circumstances, we have no quarrel with the District Court’s sua spowte deletion of Greenberg’s fraud claim.

The District Court also properly dismissed plaintiffs’ cause of action for “fraudulent scheme,” the elements of which purportedly are (1) the accomplishing of a lawful purpose (2) by unlawful means. New York does not recognize such a cause of action. At most, the cases on which plaintiffs rely—an 1882 decision of the New York State Court of Appeals, Rich v. New York Cent. & Hudson River R.R. Co., 87 N.Y. 382 (1882), and two decisions citing Rich, Albemarle Theatre, Inc. v. Bayberry Realty Corp., 27 A.D.2d 172, 277 N.Y.S.2d 505 (1st Dep’t 1967) and North Shore Bottling Co. v. C. Schmidt & Sons, Inc., 22 N.Y.2d 171, 292 N.Y.S.2d 86, 239 N.E.2d 189 (1968)—recognize that a contractual relationship sometimes gives rise to a legal common law duty extraneous to the contract, Albemarle, 27 A.D.2d at 177, 277 N.Y.S.2d at 511, the intentional violation of which may constitute a tort. None of the cited cases identify an independent cause of action for “fraudulent scheme,” as defined by plaintiffs. Indeed, plaintiffs’ claim appears to be simply a repackaging of the same allegations made in their other causes of action. The District Court did not err in dismissing this claim.

Plaintiffs’ remaining arguments also lack merit. The District Court did not abuse its broad discretion in precluding expert witnesses from both plaintiffs and defendants on the issue of the methodology used in the “Consensus Report” and in limiting the scope of the testimony of a fact witness on that same issue. See generally E.R. Squibb & Sons, Inc. v. Lloyd’s & Cos., 241 F.3d 154, 167 (2d Cir. 2001); Olin Corp. v. Ins. Co. of N. Am., 221 F.3d 307, 319 (2d Cir. 2000) (“[E]ven an erroneous evidentiary ruling will not lead to reversal unless affirmance would be inconsistent with substantial justice.” (internal quotation marks omitted)). While we might find error in the District Court’s limitation of plaintiffs’ proof of damages, any such error was harmless in light of plaintiffs’ inability to establish defendants’ liability. We also find no abuse of discretion in the District Court’s denial of plaintiffs’ motions for leave to amend their complaint, which were made after the filing of summary judgment motions and again at trial. See Grace v. Rosenstock, 228 F.3d 40, 53-54 (2d Cir. 2000), cert. denied, 532 U.S. 923, 121 S.Ct. 1362, 149 L.Ed.2d 290 (2001); Commander Oil Corp. v. Bario Equip. Corp., 215 F.3d 321, 333 (2d Cir.), cert. denied, 531 U.S. 979, 121 S.Ct. 427, 148 L.Ed.2d 436 (2000); Cahill v. O’Donnell, 75 F.Supp.2d 264, 279 (S.D.N.Y. 1999) (“Our Circuit has consistently found prejudice and denied amendments where discovery has already been completed and summary judgment motions have been filed.”). Lastly, we find no abuse of discretion in the District Court’s denial of plaintiffs’ motion to compel production of documentary discovery, some of which was plainly irrelevant or privileged, and some of which was duplicative of previously produced material. See generally United States v. Yonkers *638Bd. of Educ., 946 F.2d 180, 185 (2d Cir. 1991).

We have examined all of the plaintiffs’ contentions and find them to be without merit. For the reasons set forth, the judgment of the District Court is hereby AFFIRMED.