Pride Transportation (“Pride”) appeals a summary judgment for its primary and excess insurers, Continental Casualty Company (“Continental”) and Lexington Insurance Company (“Lexington”), alleging that the insurers breached their contracts by failing to continue to defend and indemnify Pride after settling a claim, against an employee, that had exhausted the policies. In addition, Pride alleges that the insurers’ handling of the settlement violated Texas Insurance Code Section 541.060. Because Pride failed to raise a genuine issue of material fact as to either claim, we affirm.
I.
In October 2006, in Wise County, Texas, Krystal Harbin, a driver for Pride, struck Wayne Hatley’s pickup truck when Hatley slowed down for a dust cloud caused by a gravel spill. The impact caused Hatley to collide with a crane truck; he was severely injured and is a paraplegic with limited use of his upper extremities.
Pride is a large-fleet interstate motor carrier headquartered in Utah. It carried a primary insurance policy issued by Continental with a limit of $1 million and an excess policy with Lexington for $4 million. Harbin was named as an additional insured on both policies, which covered defense and indemnity until funds were exhausted by payments of judgments or settlements.
II.
Hatley and his wife sued Harbin and Pride, among others, in state court in Wise County for negligence, seeking damages for medical expenses, loss of earnings, physical impairment, disfigurement, pain and mental anguish, loss of household services, and loss of consortium. As the primary insurer, Continental stepped in to defend Pride and Harbin and began investigating the accident.1
Harbin’s counsel estimated the value of the case as $8-10 million, and Pride’s counsel acknowledged the “real possibility” that liability was over $5 million. Hatley’s medical expenses alone exceeded the primary policy limits. The Hatleys’ counsel had recently won jury verdicts in Wise County for over $25 million in similar cases; and the insured parties recognized that there was a risk of high jury verdicts in that forum. Counsel, representing both Pride and Harbin at the time, reported to Continental in January 2007 that it might *349be worthwhile to seek an early settlement, although more investigation was needed.
During Harbin’s April 2007 deposition, it became clear that she had falsified her driver logs to avoid restrictions on the hours she could work.2 That fact caused concern for increased exposure to liability. Pride’s separate counsel admitted that Harbin would be a bigger target for liability than would Pride. In about May 2007, Lexington told Pride that the claim might exceed the excess policy’s limits.
In June 2007, Harbin received a settlement demand from the Hatleys for the total of the policies, $5 million (the “Harbin Settlement”); in exchange for that sum, the Hatleys would release Harbin from liability. The Hatleys’ demand expressly noted that Pride was not included in the Settlement.3 Relatedly, Harbin would remain exposed to any cross-claims for indemnity pursued by Pride. The deadline to accept the demand was July 20, 2007.
Because the sum was larger than the primary policy, Continental had to tender the $1 million to Lexington in order for Lexington to respond to the demand. Pride requested that Continental complete the tender, hoping that would allow Lexington to seek a counter-offer. Continental tendered on July 17,4 after which Lexington took control of the defense and asked the Hatleys’ counsel to consider a settlement that included Pride; the Hat-leys refused.
Pride opposed accepting the Harbin Settlement and asked Lexington to put a formal counter-offer in writing for a release of both insureds for $5 million. Lexington informed Pride and Harbin that a counteroffer would need to be agreed to by both insured parties. Harbin rejected that proposal and demanded Lexington accept, which it did on July 20.
The insurers notified Pride that, because the policies were exhausted, they would withdraw their defense of Pride.5 On August 28, Lexington sued in the United States District Court for the Northern District of Texas (the “Northern District”) for a declaratory judgment regarding its coverage obligations to Pride.
On August 30, Pride filed a cross-claim for indemnity against Harbin in the Hat-leys’ underlying suit.6 On August 31, Pride sought a declaratory judgment in Utah state court that the insurers had an ongoing duty to defend and indemnify it in that case. The declaratory-judgment action was removed to Utah federal court, *350then transferred to the Northern District in January 2008.
Lexington and Continental counterclaimed.7 Pride’s amended complaint alleged breaches of contract, fiduciary duty, good faith and fair dealing, and violation of the Texas Insurance Code. The district court granted summary judgment for the insurers, denied Pride’s Federal Rule of Civil Procedure 59(e) motion to alter or amend, and granted Continental’s motion to alter or amend for attorney’s fees.
Pride appeals the summary judgment, arguing that there is a genuine issue of material fact whether the insurers (1) breached their contracts by failing to continue to defend and indemnify Pride after the Harbin Settlement exhausted the policies and (2) violated Section 541.060 of the Texas Insurance Code by their handling of the Settlement. Pride also appeals the dismissal of its motion to alter or amend.
III.
“We review a summary judgment de novo, applying the same standard as the district court.” United States ex rel. Jamison v. McKesson Corp., 649 F.3d 322, 326 (5th Cir.2011). Summary judgment is appropriate where, viewing the evidence in the light most favorable to the nonmovant, “there is no genuine dispute as to any material fact and the movant is entitled to judgment as a matter of law.” Fed. R.CivP. 56(a); Songer v. Dillon Res., Inc., 618 F.3d 467, 471 (5th Cir.2010). Furthermore, “it is an elementary proposition, and the supporting cases too numerous to cite, that this court may affirm the district court’s judgment on any grounds supported by the record.” 8
This case is in federal court on diversity jurisdiction, so Texas substantive law governs. Packard v. OCA, Inc., 624 F.3d 726 (5th Cir.2010). This court looks to the decisions of the Texas Supreme Court to determine Texas law, and where that court has not ruled, the panel “must determine, to the best of our ability, what the highest court of the state would do.”9 Although the decisions of the intermediate state courts of appeals are not binding precedent in this regard, they can be instructive. Am. Int’l Specialty Lines Ins. Co. v. Rentech Steel, L.L.C., 620 F.3d 558, 566 (5th Cir.2010).
Insured parties have limited recourse against insurers in Texas for the handling of third-party insurance claims. There is no duty of good faith and fair dealing owed to the insured in this context — common law duties are limited to contractual obligations and the Stowers10 duty to accept a reasonable settlement demand.11 In Texas, an insurer is liable under Stowers for rejecting a demand where
(1) the claim against the insured is within the scope of coverage,
(2) the demand is within the policy limits, and (3) the terms of the demand are *351such that an ordinarily prudent insurer would accept it, considering the likelihood and degree of the insured’s potential exposure to an excess judgment.
Am. Physicians Ins. Exch. v. Garcia, 876 S.W.2d 842, 849 (Tex.1994). “[A] Stowers settlement demand must propose to release the insured fully in exchange for a stated sum of money.” Id. at 848.
In Farmers Insurance Co. v. Soriano, 881 S.W.2d 312, 315 (Tex.1994), the court concluded “that when faced with a settlement demand arising out of multiple claims and inadequate proceeds, an insurer may enter into a reasonable settlement with one of the several claimants even though such settlement exhausts or diminishes the proceeds available to satisfy other claims.” The reasonableness of the settlement is determined “considering solely the merits of the [settled claim] and the potential liability of its insured on [that] claim.” Id. at 316. In Travelers Indemnity Co. v. Citgo Petroleum Corp., 166 F.3d 761 (5th Cir.1999), we interpreted Texas law to extend Soriano to cases with multiple insured defendants; we held that “an insurer is not subject to liability for proceeding, on behalf of a sued insured, with a reasonable settlement ... once a settlement demand is made, even if the settlement eliminates ... coverage for a co-insured as to whom no Stowers demand has been made.” Id. at 768.
The insurer cannot be liable for failing to settle remaining claims “unless there is evidence that either (1) [the insurer] negligently rejected a demand from the [claimant] within policy limits; or (2) the [initial settlement demand] was itself unreasonable.” Soriano, 881 S.W.2d at 315. The test for whether the settlement was unreasonable invokes the same standard as did Stowers: “that a reasonably prudent insurer would not have settled the [initial] claim when considering solely the merits of [that] claim and the potential liability of its insured on the claim.” Id. at 316.
The parties agree that the insurers did not reject any demands for Pride or Harbin. Instead, this case involves the insurers’ liability for accepting a demand. Although the Stowers duty imposes liability on insurers who reject reasonable demands covered under their policies, we decline to use this case, as Pride wishes, to extend the Stowers duty to impose liability on insurers for accepting demands.
Pride’s common-law claims thus must rest on the insurers’ contractual duties. The parties do not dispute that the insurers are absolved of their duty to defend an insured party once the policy has been exhausted by judgments or settlements; nor do they gainsay that the insurers have a contractual right to settle claims as they deem appropriate.12 The parties also agree that the Harbin Settlement exhausted both policies.
The dispute at the heart of Pride’s breach-of-contract claim is that the insurers’ acceptance of the Harbin Settlement was unreasonable in violation of the policies and that, as a result, the insurers were never dismissed from their contractual duties to defend Pride. Notably, Pride does not contend that the Settlement was per se unreasonable because the Insurers settled for Harbin and not Pride.13 In*352stead, Pride attempts to distinguish the instant case from Citgo and Soriano, in which the reasonableness of the other insured’s settlement was undisputed.14 Pride asserts that the reasonableness of the Settlement is a question of fact for a jury and not appropriate for summary judgment.
Pride focuses on Stowers, arguing that the Settlement was not a valid Stowers demand, so the insurers lose their defense for accepting. Pride asserts that, in the absence of a safe harbor, the reasonableness of the Settlement, which left Harbin and Pride open to further liability, presents a question of fact. Though the insurers likely would have faced Stowers liability had they rejected the Hatleys’ demand, see Soriano, 881 S.W.2d at 815, this court does not need to determine whether there was a valid Stowers demand.
“Under Soriano and the explicit language of the policy, [the insurers] had a right to settle when [they were] presented with a demand "within [their] policy limits.” Citgo, 166 F.8d at 768. Because Pride does not allege that the insurers negligently rejected a demand that included Pride, the insurers can be liable to Pride only if the Harbin Settlement was unreasonable. See Soriano, 881 S.W.2d at 315. “To be unreasonable, [Pride] must show that a reasonably prudent insurer would not have settled the [Harbin] claim when considering solely the merits of the [Harbin] claim and the potential liability of its insured on the claim.” Id. at 316.
Pride’s only argument that the Harbin Settlement is unreasonable rests on the residual liability Harbin faces in an indemnity claim by Pride. That argument fails to create an issue of fact on reasonableness, because the Lexington policy explicitly exempts claims or suits brought by one insured against another.15 “[A]n insurer has no duty to settle a claim that is not covered under its policy.” Garcia, 876 S.W.2d at 848. This court also interpreted Texas law in St. Paul Fire & Marine Ins. Co. v. Convalescent Services, Inc., 193 F.3d 340, 345 (5th Cir.1999), rejecting the notion “that the insurer has a duty to consider claims that are excluded from coverage when making its determination of whether a settlement is reasonable.”
In the absence of liability on the part of Harbin to her former employer, Pride fails to create an issue of fact as to the reasonableness of the Settlement. See Citgo, 166 F.3d at 765. Because of the likelihood and degree of potential exposure to excess judgment for Harbin, the Settlement was reasonable as a matter of law and did not result in a breach of the insurance contracts.16 The evidence showed that Harbin falsified her driver logs in order to make deliveries on time; Wayne Hatley was a paraplegic with limited use of his upper extremities and facing lifetime medical costs over $4 million; the Hatleys’ lawyer *353had obtained jury verdicts of about $25 million in Wise County for similar accidents; and counsel for Pride and Harbin had estimated a case value exceeding the insurance coverage. As the district court stated, “Stowers — duty bound or not, the insurers’ acted reasonably in accepting the Hatleys’ demand despite the fact that Pride remained exposed.” Pride Transp. v. Cont’l Cas. Co., 804 F.Supp.2d 520, 530 (N.D.Tex.2011).
IV.
“A motion to alter or amend the judgment under Rule 59(e) must clearly establish either a manifest error of law or fact or must present newly discovered evidence and cannot be used to raise arguments which could, and should, have been made before the judgment issued.”17 We generally review for abuse of discretion the denial of a Rule 59(e) motion. Schiller, 342 F.3d at 566.
Pride filed a Rule 59(e) motion to alter or amend after the grant of summary judgment, asserting that the district court erred in its failure to consider, as part of the reasonableness inquiry, the terms of the Settlement that expressly excluded Pride’s liability for Harbin’s conduct. Pride relies on an opinion from the Southern District of Texas18 that was decided after the instant summary judgment was granted. Without deciding whether that decision is persuasive authority, we note that nothing in Tristar suggests that the district court a quo denied Pride’s motion based on “an erroneous view of the law or on a clearly erroneous assessment of the evidence.” Ross v. Marshall, 426 F.3d 745, 763 (5th Cir.2005).
Tristar is similar to the present case in that it involved an insurer that settled on behalf of some of the insureds, exhausting the policy and leaving Tristar without coverage. Unlike the Hatleys, however, the plaintiffs in the underlying lawsuit in Tris-tar made an initial demand that would have released all the defendants, including Tristar. Tristar, 2011 WL 2412678, at *1. After rejecting the first demand, the insurers accepted a second offer that released all the insureds except Tristar. Id. The court denied summary judgment as to the insurer’s Stowers liability for rejecting the first demand. Considering not just the terms of the initial demand but also the accepted demand, the court held that the reasonableness of the first demand was a disputed question of fact. Id. at *4.
Pride seeks to rely on Tristar for the proposition that, when determining reasonableness in cases involving multiple insured parties, this court should consider the demand’s terms regarding the liability of all insured parties. Unlike the plaintiffs in Tristar, however, the Hatleys never made a settlement demand that included Pride, nor is the instant case about the insurers’ Stowers liability for rejecting a demand. The district court did not abuse its discretion in denying Pride’s motion to alter or amend.
V.
Pride contends that the district court erred in granting summary judgment for the insurers on Pride’s claim under Section 541.060(a)(2) of the Texas Insurance Code § 541.060(a)(2), which makes it “an unfair method of competition or an unfair or deceptive act or practice in the business of *354insurance” to “fai[l] to attempt in good faith to effectuate a prompt, fair, and equitable settlement” of a claim. Pride alleges that the insurers violated their statutory duty of good faith and fair dealing by not settling Harbin’s liability to Pride.
The good-faith duty under Section 541.060 is triggered only where “(1) the policy covers the claim, (2) the insured’s liability is reasonably clear, (3) the claimant has made a proper settlement demand within policy limits, and (4) the demand’s terms are such that an ordinarily prudent insurer would accept it.” Rocor Int'l, Inc. v. Nat'l Union Fire Ins. Co. of Pittsburgh, PA, 77 S.W.3d 253, 255 (Tex.2002) (interpreting a previous version of the statute). Texas imported the common-law standard from Stowers, holding that, unlike many jurisdictions, “in Texas, the common law imposes no duty on an insurer to accept a settlement demand in excess of policy limits or to make or solicit settlement proposals.” Id. at 261.
We can assume arguendo that the Harbin Settlement triggered duties under Section 541.060: The policies covered the Hatleys’ claim against Harbin; Harbin’s liability was reasonably clear; the demand was within the policy limits of $5 million;19 and as determined already, the terms of the Harbin Settlement were such that an ordinarily prudent insurer would accept them.20 The question is whether Pride raised an issue of material fact as to the insurers’ good-faith effort to effect a prompt, fair, and equitable settlement.
As to Lexington, Pride only speculates, without evidence, that Lexington’s sole mission was to extricate itself from the case as quickly as possible. “In short, conclusory allegations, speculation, and unsubstantiated assertions are inadequate to satisfy the nonmovant’s burden.” 21
Pride attempts to create an issue of fact as to Continental’s good faith by offering that the claim was without a claims adjuster for a month, and Continental did not immediately tender its policy limits to Lexington. Neither of these facts is sufficient to defeat summary judgment. Although there was a month during which a permanent adjuster was not assigned to the Hatleys’ claims, the unit manager at Continental handled all interim claims resulting from the accident, and the Hatleys did not make a demand until after the adjuster had been replaced. As for the date of Continental’s tender to Lexington on July 17, 2007 — before the deadline— Pride offers no evidence that Continental was acting in bad faith. To the contrary, Continental produced evidence that it was preparing the defense and completing due diligence until the tender.
The summary judgment is AFFIRMED.