KING, Circuit Judge:

Larry M. Gentilello, M.D., a tenured professor at the University of Texas Southwestern Medical Center, brought suit under 42 U.S.C. § 1983 against his supervisors, alleging that he was wrongfully demoted without due process of law in violation of the Fourteenth Amendment. The district court granted the Defendants' motion for judgment on the pleadings and denied Gentilello leave to file an amended or supplemental complaint. Because we agree with the district court that Gentilello has failed to allege sufficient facts to state a claim for the deprivation of a protected property interest without due process of law, we affirm.

I. BACKGROUND

Appellant Gentilello was at all relevant times, a tenured professor of surgery at the University of Texas Southwestern Medical Center at Dallas ("UT Southwestern"). Until March 2007, Gentilello also held the positions of Chair of the Division of Burns, Trauma and Critical Care and the Distinguished C. James Carrico, M.D. Chair in Trauma (the "Chair Positions"). Gentilello alleged that Robert V. Rege, M.D., Chairman of the Department of Surgery at UT Southwestern, and Alfred G. Gilman, M.D., Ph.D., Dean of the UT Southwestern Medical School, wrongfully removed him from the Chair Positions. According to Gentilello, the demotion occurred after Gentilello voiced his concerns to Rege about what he considered to be substandard patient care at Parkland Hospital, a hospital served by UT Southwestern. Gentilello alleged that Rege and Gilman demoted him in retaliation for speaking out about the "improper and illegal" practices at Parkland Hospital.

Gentilello filed a complaint on September 13, 2007, against Rege and Gilman (the "Defendants"), seeking damages under 42 U.S.C. § 1983 for two claims of alleged civil rights violations in connection with his demotion. Gentilello claimed that the Defendants retaliated against him for exercising his right to free speech in violation of the First Amendment, and that the Defendants deprived him of his constitutionally-protected property interest in the Chair Positions without due process of law in violation of the Fourteenth Amendment. In response to the Defendants' pre-answer motion to dismiss pursuant to Federal Rule of Civil Procedure 12(b)(6), Gentilello filed an Amended Complaint on October 22, 2007. The district court granted the Defendants' motion to dismiss Gentilello's First Amendment retaliation claim, but denied it as to his due process claim, stating that Gentilello's allegations sufficed to establish that he had been denied due process in connection with his demotion. Subsequently, on August 29, 2008, the Defendants filed an Answer in which they asserted, inter alia, a qualified immunity defense. On March 20, 2009, after the deadline for amendment of the pleadings in the district court's scheduling order, but before the deadline for dispositive motions, the Defendants moved for judgment on the pleadings pursuant to Rule 12(c). The Defendants contended that Gentilello had failed to allege sufficient facts to establish that he had a constitutionally-protected property interest in the Chair Positions, and, therefore, he had failed to allege that the Defendants violated a clearly established right as required to overcome their qualified immunity defense.

Before the district court ruled on this motion, Gentilello moved for leave to supplement the pleadings. In his proposed Supplemental Complaint, Gentilello asserted a separate claim for damages under § 1983 against Defendants Rege and Gilman for wrongfully removing Gentilello from trauma call rotation at Parkland Hospital on July 29, 2008. Gentilello alleged that his removal was retaliatory, "arbitrary and capricious," and resulted in further deprivation of his property rights without due process of law in violation of the Fourteenth Amendment.

On November 13, 2009, the district court entered an order granting the Defendants' motion for judgment on the pleadings and dismissing Gentilello's claims with prejudice. The district court held that "Plaintiff has not plead[ed] the existence of an employment contract, nor has Plaintiff even plead[ed] facts that the employment at-will relationship was altered in any manner." Therefore, Gentilello had not sufficiently pleaded the existence of a constitutionally-protected property interest to state a due process violation and the Defendants were entitled to qualified immunity. The district court also denied Gentilello leave to amend his complaint to cure the deficiencies in his pleadings, stating that it was "unwilling to allow an amendment more than a year after Plaintiff initially amended his complaint." The district court also denied Gentilello's motion for leave to file a supplemental pleading to assert a claim in connection with his removal from trauma call rotation at Parkland Hospital, finding the motion untimely. Gentilello appeals.

II. DISCUSSION

We review a district court's ruling on a Rule 12(c) motion for judgment on the pleadings de novo. Great Plains Trust Co. v. Morgan Stanley Dean Witter Co., 313 F.3d 305, 312 (5th Cir. 2002) (citing Hughes v. Tobacco Inst., Inc., 278 F.3d 417, 420 (5th Cir. 2001)). We evaluate a motion under Rule 12(c) for judgment on the pleadings using the same standard as a motion to dismiss under Rule 12(b)(6) for failure to state a claim. Doe v. MySpace, Inc., 528 F.3d 413, 418 (5th Cir. 2008). "`[T]he central issue is whether, in the light most favorable to the plaintiff, the complaint states a valid claim for relief.'" Id. (quoting Hughes, 278 F.3d at 420). To avoid dismissal, a plaintiff must plead sufficient facts to "`state a claim to relief that is plausible on its face.'" Ashcroft v. Iqbal, ___ U.S. ___, 129 S.Ct. 1937, 1949, 173 L.Ed.2d 868 (2009) (quoting Bell Atl. Corp. v. Twombly, 550 U.S. 544, 570, 127 S.Ct. 1955, 167 L.Ed.2d 929 (2007)). "A claim has facial plausibility when the plaintiff pleads factual content that allows the court to draw the reasonable inference that the defendant is liable for the misconduct alleged." Id. "We do not accept as true conclusory allegations, unwarranted factual inferences, or legal conclusions." Plotkin v. IP Axess Inc., 407 F.3d 690, 696 (5th Cir. 2005); see also Iqbal, 129 S.Ct. at 1950 ("While legal conclusions can provide the framework of a complaint, they must be supported by factual allegations.").

A public official performing a discretionary function is entitled to qualified immunity in a civil action for damages, provided his conduct does not "violate clearly established federal statutory or constitutional rights of which a reasonable person would have known." Harlow v. Fitzgerald, 457 U.S. 800, 818, 102 S.Ct. 2727, 73 L.Ed.2d 396 (1982). In determining whether a defendant is entitled to qualified immunity, we decide whether facts alleged or shown by the plaintiff make out a violation of a constitutional right, and whether that right was "clearly established" at the time of the defendant's alleged misconduct. Pasco ex rel. Pasco v. Knoblauch, 566 F.3d 572, 579 (5th Cir. 2009). The district court held that the defendants were entitled to qualified immunity because Gentilello had not alleged sufficient facts to state a constitutional violation. We agree. See Johnson v. Johnson, 385 F.3d 503, 525 (5th Cir. 2004) ("Of course, the defendant's conduct cannot constitute a violation of clearly established law if, on the plaintiffs version of the facts, there is no violation at all.").

To state a Fourteenth Amendment due process claim under § 1983, "a plaintiff must first identify a protected life, liberty or property interest and then prove that governmental action resulted in a deprivation of that interest." Baldwin v. Daniels, 250 F.3d 943, 946 (5th Cir. 2001). To enjoy a property interest in employment, an employee must "have a legitimate claim of entitlement" created and defined "by existing rules or understandings that stem from an independent source such as state law. . . ." Bd. of Regents v. Roth, 408 U.S. 564, 577, 92 S.Ct. 2701, 33 L.Ed.2d 548 (1972). In Texas, there exists a presumption that employment is at-will, unless that relationship has been expressly altered by contract or by express rules or policies limiting the conditions under which an employee may be terminated. Muncy v. City of Dallas, 335 F.3d 394, 398 (5th Cir. 2003) (citations omitted). "[A]bsent a specific agreement to the contrary, employment may be terminated by the employer or the employee at will, for good cause, bad cause, or no cause at all." Montgomery Cnty. Hosp. Dist. v. Brown, 965 S.W.2d 501, 502 (Tex. 1998).

Here, it is not disputed that Gentilello, as a tenured professor, had a protected property interest in his continued employment at UT Southwestern. See Roth, 408 U.S. at 576-77, 92 S.Ct. 2701. However, the due process clause does not protect Gentilello's specific job duties or responsibilities absent a statute, rule, or express agreement reflecting an understanding that he had a unique property interest in those duties or responsibilities. See DePree v. Saunders, 588 F.3d 282, 289-90 (5th Cir. 2009); Kelleher v. Flawn, 761 F.2d 1079, 1087 (5th Cir. 1985) (rejecting a public employee's claim of entitlement to specific duties, where neither state law nor the employee's contract supplied a basis for a claim of entitlement to those duties). Therefore, to establish a due process claim in connection with his demotion, Gentilello was required to point to some state or local law, contract, or understanding that created a property interest in the Chair Positions. "Absent a property interest, there is nothing subject to due process protections and our inquiry ends." Cabrol v. Town of Youngsville, 106 F.3d 101, 105 (5th Cir. 1997).

Nowhere in Gentilello's Complaint, filed September 13, 2007, his Amended Complaint, filed October 22, 2007, or his proposed Supplemental Complaint, filed April 21, 2009, did Gentilello plead the factual basis for his alleged property interest in the Chair Positions. In his Amended Complaint, Gentilello alleged the bare legal conclusion that the Defendants "wrongfully removed Plaintiff from his [Chair Positions], positions in which Plaintiff had a constitutionally protected property interest in occupying for a previously-determined period of time." He further alleged that "Defendants' conduct caused Plaintiff to be deprived of his vested, constitutionally protected property right in his [Chair Positions]," and as a result, that he "was not merely deprived of duties and responsibilities, but rather, was deprived of the economic interests in and benefits associated with such positions." Gentilello did not substantiate these allegations by pointing to any ordinance, official policy, state or local law, contract, or other enforceable agreement to support his claim of entitlement to the Chair Positions. Therefore, his pleadings fail to state a due process claim. See Blackburn v. City of Marshall, 42 F.3d 925, 940 (5th Cir. 1995) ("Because [plaintiff] does not allege that his property interest . . . stems from a state statute or regulatory scheme, a contract, or any other independent source, we find that [plaintiff] has failed to allege a property interest protected by the Due Process Clause of the Fourteenth Amendment.").

Nor did Gentilello alert the district court to the factual basis for his claim of entitlement to the Chair Positions in his extensive briefing in opposition to Defendants' motion for judgment on the pleadings. At best, Gentilello asserted that he had a property interest in the Chair Positions "based upon letters from Defendants," the contents of which he has not disclosed to the district court or even (when we made inquiry at oral argument) to this court. Apparently as a result of these letters, Gentilello asserted that he had a contract with UT Southwestern "which was subject to certain rules and regulations" — which Gentilello has not identified — "that required `good cause' before his chaired positions could be terminated." Contrary to Gentilello's contentions, these "[thread-bare recitals of the elements of a cause of action, supported by mere conclusory statements, do not suffice" to state a due process claim. Iqbal, 129 S.Ct. at 1949 (citing Twombly, 550 U.S. at 555, 127 S.Ct. 1955).

Gentilello also contends that the district court erred in denying leave to amend his pleadings as an alternative to dismissal. In response to the Defendants' motion for judgment on the pleadings, Gentilello averred that, if the district court found his pleadings deficient, he could submit "additional evidence to show a constitutionally-protected right to his position because he may only be terminated from this position for cause." Accordingly, Gentilello asserted that good cause exists to allow him to amend his complaint. We review the district court's denial of leave to amend for abuse of discretion. Torch Liquidating Trust ex rel. Bridge Assocs. L.L.C. v. Stockstill, 561 F.3d 377, 390 (5th Cir. 2009). Where, as here, the movant seeks leave to amend after the pleadings deadline in the district court's scheduling order, the movant must demonstrate good cause. S W Enters., L.L.C. v. South-Trust Bank of Ala., 315 F.3d 533, 535-36 (5th Cir. 2003).

The district court was "unwilling to allow an amendment more than a year after Plaintiff initially amended his complaint," citing Jacquez v. Procunier, 801 F.2d 789, 792 (5th Cir. 1986) ("[I]f the protections afforded public officials are not to ring hollow, plaintiffs cannot be allowed to continue to amend or supplement their pleadings until they stumble upon a formula that carries them over the threshold."). Gentilello argues that, because the district court initially found his pleadings sufficient to state a claim, he had no reason to amend to assert additional facts regarding his property interest in the Chair Positions until the Defendants moved for judgment on the pleadings. Nonetheless, we find that the district court did not abuse its discretion in denying Gentilello leave to amend. Throughout his briefing in opposition to the Rule 12(c) motion, Gentilello contended that his pleadings sufficed to state a due process claim, adamantly asserted that he was not required to plead additional facts to support his claim of entitlement to the Chair Positions, and failed to apprise the district court of the facts that he would plead in an amended complaint, if necessary, to cure any deficiencies in his pleadings. Moreover, Gentilello failed to tender a proposed Amended Complaint setting forth these facts. Gentilello's counsel professed at oral argument before this court that evidence purportedly establishing a property interest in the Chair Positions was in Gentilello's possession. Gentilello had ample opportunity to present this evidence to the district court prior to dismissal, but he refused to do so. In similar circumstances, we have had little difficulty affirming a district court's denial of leave to amend. See, e.g., Goldstein v. MCI WorldCom, 340 F.3d 238, 254-55 (5th Cir. 2003); McKinney v. Irving Indep. School Dist., 309 F.3d 308, 315 (5th Cir. 2002). "At some point a court must decide that a plaintiff has had a fair opportunity to make his case; if, after that time, a cause of action has not been established, the court should finally dismiss the suit." Jacquez, 801 F.2d at 792. Accordingly, we decline to remand to allow Gentilello further opportunity to state his claim.

Finally, we find that the district court did not err in denying Gentilello's request for leave to supplement his pleadings. The decision to grant or deny leave to supplement is within the sound discretion of the district court Burns v. Exxon Corp., 158 F.3d 336, 343 (5th Cir. 1998) ("the court may permit a supplemental pleading") (emphasis in original). Gentilello did not move for leave to file his proposed Supplemental Complaint until April 21, 2009, almost nine months after he was removed from the trauma call list at Parkland Hospital, the action giving rise to his new claim, and nearly four months after the pleadings deadline in the district court's scheduling order. He has provided no justification for the delay. The district court reasonably concluded that Gentilello's motion was untimely. See Lewis v. Knutson, 699 F.2d 230, 239-40 (5th Cir. 1983) (district court did not abuse its discretion in denying leave to supplement where, inter alia, plaintiff moved to supplement five months after the occurrence giving rise to the proposed supplemental claim).

III. CONCLUSION

For the foregoing reasons, we AFFIRM the judgment of the district court.