Mexican actor Robert Cavazos wrote on his Facebook page that he encountered Spacey at the bar of London's Old Vic Theatre, where Spacey was artistic director, and the actor tried to fondle him against his will.
"It was more common for this guy, when he was in the bar of his theater, grabbing whoever caught his attention," Cavazos wrote. "I didn't stand for it, but I know some people who were afraid to stop it."
Cavazos declined an interview request. There was no immediate reply to a request for comment from representatives for Spacey, who was artistic director from 2004-15.
In a statement Tuesday, the theater expressed "deep dismay" at the allegations and said "inappropriate behavior by anyone working at The Old Vic is completely unacceptable."
In recent days, Hollywood has reacted swiftly to allegations of sexual harassment and assault: Harvey Weinstein was fired from the company he founded within days after initial reports of sexual harassment were published in The New York Times earlier this month.
Weinstein has denied engaging in any non-consensual sexual contact.
Dozens of women, including actresses Selma Blair and Rachel McAdams, have alleged that writer and director James Toback sexually harassed or assaulted them.
Toback has denied the allegations.
On Tuesday, however, the Beverly Hills Police Department said it was investigating both men after receiving "multiple complaints," although the department did not specify the nature of the complaints.
On Monday, Netflix said it would end "House of Cards" after its upcoming sixth and final season, although the streaming network said the decision was made before the BuzzFeed News report on Spacey last weekend. The network has not commented on plans for a Gore Vidal biopic starring Spacey that is currently in production.
The pause in production Tuesday shadows the fate of the last season.
Also Tuesday, CBS said it is "looking into" a claim by actress and reality star Ariane Bellamar that Emmy-winning "Entourage" star Piven groped her on two occasions.
On her Twitter account Monday, Bellamar alleged that one encounter took place in Piven's trailer on HBO's "Entourage" set and the other occurred at the Playboy Mansion.
Piven, who stars in the new CBS series "Wisdom of the Crowd," said in a statement that he "unequivocally" denies the "appalling allegations being peddled about me."
"It did not happen. It takes a great deal of courage for victims to come forward with their histories, and my hope is that the allegations about me that didn't happen, do not detract from stories that should be heard," he said.
In a Monday interview with The Associated Press, Piven said he was glad people had come forward with allegations against Harvey Weinstein and that he had never been in that situation.
HBO, which aired the 2004-11 series, said in a statement that it was unaware of Bellamar's allegations until they were reported by media.
"Everyone at HBO and our productions is aware that zero tolerance for sexual harassment is our policy. Anyone experiencing an unsafe working environment has several avenues for making complaints that we take very seriously," the channel said.
Bellamar's credits include "Suicide Squad" and "The Hangover Part III" and the reality series "Beverly Hills Nannies."