"Those of us who crossed paths with (Spacey) in London when he was director of the Old Vic know a whole lot more people will find the courage to tell their stories in the coming days and weeks," he said.
"It wouldn't surprise me if there were similar numbers to Weinstein's," he added, referring to the dozens of women who have accused Hollywood mogul Harvey Weinstein of sexual assault and harassment, unleashing a torrent of similar accusations against a growing list of rich and powerful men.
SPACEY, WEINSTEIN Y EL ACOSO ENDÉMICO DEL QUE NO HABLAMOS EN EL TEATRO MEXICANO
Harvey Weinstein. Kevin Spacey. Max...
Posted by Roberto Cavazos on Monday, 30 October 2017
It comes as the Old Vic Theatre appeals to employees to come forward if they experienced something at the theatre they felt they could not discuss at the time.
"The Old Vic would like to respond to recent media reports by making it clear that we are deeply dismayed to hear the allegations levied against Kevin Spacey, who was Artistic Director from 2004-2015," the theatre said in a statement.
"We want our employees to feel confident, valued and proud to be part of The Old Vic family. Any behaviour we become aware of which contravenes these goals will not be tolerated."
Spacey has not responded to the recent allegations. However the star of the Netflix series House of Cards, has apologised to Rapp on Twitter and come out as gay - drawing fierce criticism from some who accuse him of trying to deflect attention from his alleged behaviour
Following the Rapp allegations he said he was "beyond horrified" to hear the story and did not remember the encounter.
"But if I did behave then as he describes, I owe him the sincerest apology for what would have been deeply inappropriate drunken behaviour."
Cavazos, 35, is a stage and screen actor whose credits include the films "Rush" and "El Beso" and a guest appearance on the British TV series "Doctor Who."
According to his profile, he acted in three plays at the Old Vic during Spacey's tenure as artistic director, from 2004 to 2015.
The first was in 2008, when he would have been about 26 and Spacey about 49. He said he fended off two "unpleasant" advances from Spacey that "bordered on harassment," but that others were afraid to do so.
"I can't even remember how many people told me the same story: Spacey invited them to meet with him to 'talk about their careers.' When they arrived at the theatre, he had prepared a champagne picnic on the stage, beautifully lit," he wrote, in allegations first posted to Facebook on Monday and repeated Tuesday on Twitter.
"Each story varied in how far the picnic went, but the technique was the same. More commonly, he could be found in the theatre bar, pressing up against whoever caught his eye. That's how it was with me the second time. I never gave in, but I know some people who were too scared to stop him."
Cavazos did not say when the alleged encounters took place. He said such harassment is widespread in the theatre world.
Another unnamed man has told the BBC's Victoria Derbyshire program that Spacey invited him to share his bed during a weekend in New York. He claimed he declined but woke up with the actor's arms around him on the couch.
"I was uncomfortable at best, traumatised at worst," said the man, known only as John, adding that he didn't believe anything sexual took place.
"He was in his underwear, I was fully clothed. I supposed it was some sort of New York theatre actor 'good morning,'" he said.
John said he believed the actor was trying to groom him during the time he stayed there despite him making clear he was not interested in sex.
"It seems he was grooming me," John told the BBC.
"For me, I never let on that that's what I was interested in. I never discussed it, nor did I want it.
"I was uncomfortable at best, traumatised at worst.
"He was either very stupid or predatory - or maybe a little of both."
It comes as another young barman, Daniel Beal, told The Sun he was flashed by Kevin Spacey outside a hotel where he was working in 2010 and handed a $8600 watch afterwards.
The young barman, who was 19 at the time, said he was sitting outside having a cigarette break when Spacey sat down next to him, flashed his privates and said: "It's big, isn't it?"
When he walked back into the bar to work, Beal said Spacey followed him and handed him an expensive Swiss watch he was wearing.
"I thought he was joking but he took off his watch and gave it to me," he said.
"Looking back I realise it was to keep me quiet."
Spacey had reportedly been to a production at the Chichester Festival Theatre nearby at the time. Beal said the encounter was "seedy and weird" and he sold the watch the next day.
Filmmaker Tony Montana, who won Oscars for The Usual Suspects and American Beauty, also claimed Spacey fondled his crotch in a Los Angeles pub in 2003.
Montana said: "I went up to order a drink and Kevin came up and put his arm around me. He put his hand on my crotch forcefully and grabbed my whole package."
Montana said Spacey then said: "This designates ownership."
The revelations follow a slew of complaints against movie mogul Harvey Weinstein which have encouraged other women to come forward as part of a #MeToo movement that has spread to include other parts of Hollywood, journalism and politics.