Eight singers and a dancer claim they were sexually harassed by the Spanish tenor from the late 1980s, according to the Associated Press news agency.
Only one of the women, mezzo-soprano Patricia Wulf, agreed to be named.
Domingo has denied the accusations, and the Los Angeles Opera - which he directs - has pledged to investigate with the help of "outside counsel".
"Still, it is painful to hear that I may have upset anyone or made them feel uncomfortable no matter how long ago and despite my best intentions," continued Mr Domingo.
"People who know me or who have worked with me know that I am not someone who would intentionally harm, offend, or embarrass anyone."
Six other women also claim the tenor made them feel uncomfortable by making "sexual overtures" towards them, AP reported.
Ms Wulf said he didn't physically touch her but would come up close to her every time she walked off stage and ask if she "had to go home tonight".
Another woman said Domingo put his hand down her skirt on one occasion. Three others said he forcefully kissed them.
The incidents are said to have taken place in different venues including a dressing room, a hotel room, during a meeting and at opera companies where Domingo held managerial positions.
"A business lunch is not strange," one of the singers told AP.
"Somebody trying to hold your hand during a business lunch is strange or putting their hand on your knee is a little strange. He was always touching you in some way, and always kissing you."