The Met initially suspended Mr. Levine in late 2017 after The New York Times published the accounts of several men who said that they had been sexually abused by him as teenagers; Mr. Levine denied their accusations. The Met fired him in March 2018, saying that its own investigation had “uncovered credible evidence that Mr. Levine engaged in sexually abusive and harassing conduct towards vulnerable artists in the early stages of their careers.”

Mr. Levine then sued the Met for breach of contract and defamation. He sought more than $5.8 million, noting that his 10-year contract as music director emeritus, the title he took after stepping down as music director in 2016, entitled him to a salary of $400,000 a year and an additional $27,000 per performance. The Met responded by filing a counterclaim against Mr. Levine for roughly the same amount — detailing accusations that Mr. Levine had abused or harassed people for decades, and accusing him of violating his duties to the Met and harming the institution.

A judge dismissed almost all of Mr. Levine’s defamation claims against the Met this spring, but Mr. Levine’s breach-of-contract claims may have been strengthened by the fact that his agreement with the Met did not contain a so-called “morals clause” holding him to certain standards of behavior. Mr. Levine’s lawyers, who denied all the allegations against him, argued in court papers that the contract contained no provisions that would have allowed the Met to remove Mr. Levine “due to alleged or actual misconduct or wrongdoing.”

Were the case to have entered the deposition phase, there would have been risks to both sides. The case could have put into the public record more details of the accusations against Mr. Levine, and about his closely guarded private life; before the suit was settled, Mr. Levine’s lawyers had been fighting a request by the Met for his medical records. And it could have renewed questions about what the Met knew, or should have known, about the behavior of its longtime music director, given the misconduct it said it had found evidence of.

The lawsuit was already a major public relations concern for the company. In one court filing, the Met’s lawyers said the company had incurred “significant reputational and economic harm as a result of the publicity associated with Levine’s misconduct.”