The allegations against Mr. Domingo, which were reported by The Associated Press, were made by eight singers and a dancer, all but one of whom spoke anonymously, who said that he had used his immense power in the opera world to try to pressure them into sexual relationships. Some described repeated, harassing phone calls; several said that they believed their careers had been harmed when they rebuffed him.

In a statement, Mr. Domingo called the allegations “as presented, inaccurate,” but called it “painful to hear that I may have upset anyone or made them feel uncomfortable — no matter how long ago and despite my best intentions.” He said that he believed that “all of my interactions and relationships were always welcomed and consensual,” and added that “the rules and standards by which we are — and should be — measured against today are very different than they were in the past.”

The Domingo case is reviving some of the most difficult questions of the #MeToo era: how to investigate allegations of wrongdoing, particularly those from unnamed accusers; when to cut ties with the accused and when to defer judgment; and what punishments, if any, are called for. Mr. Domingo’s stardom — as one of the Three Tenors, along with Luciano Pavarotti and José Carreras, he sang on the best-selling classical recordings of all time — only heightens the stakes.

Like their counterparts in Hollywood, politics, journalism and other fields, some of the classical music titans accused of sexual misconduct have effectively disappeared from the world stage, while others have gone on to second acts. The conductor James Levine has not performed in public since he was fired by the Metropolitan Opera last year after it found evidence of sexually abusive and harassing conduct; he settled a breach-of-contract and defamation lawsuit against the company this month. But within months of the conductor Daniele Gatti’s firing by the Royal Concertgebouw Orchestra of Amsterdam last year amid allegations of sexual harassment, he was appointed music director of the Rome Opera.

Now Mr. Domingo’s fate will hinge on several factors.

Most critical will be the outcome of an investigation by the Los Angeles Opera, which Mr. Domingo was instrumental in founding in 1986. Since 2003 he has been its general director, making him the public face of the company and its top administrator, although with his travel schedule, many of the day-to-day responsibilities of running it fall to Christopher Koelsch, its president and chief executive. Several of the accusations against Mr. Domingo concern encounters in Los Angeles, including as he began assuming power there.

The Met and several leading European companies said they would await the results of that inquiry before taking any actions of their own. But Mr. Domingo’s future will also be determined by a more intangible question: whether the good will he has built up with audiences over the decades will neutralize the damaging accusations against him.