A seventh named woman has come forward to allege she was sexually assaulted by Bill Cosby amid a snowballing furore around the comedian’s past.

Therese Serignese of Boca Raton, Florida, gave an interview to WPTV of West Palm Beach, in which she said she had been drugged and raped by the TV star in 1976, when she was 19. She alleged that Cosby, who was then headlining on the Las Vegas Strip, invited her to attend his show, and at the end of the after-party handed her three large white pills and told her to take them.

Serignese said she had felt she could not say no. “Authority figure, older man – he was 20 years older than me – ah, well, I took them. Didn’t know what they were, didn’t even ask. I was just intimidated I guess. I took them. My next memory is feeling drugged and him having sex with me.”

Serignese said Cosby let her stay in his penthouse suite for several weeks after the alleged attack.

The latest allegations add to a sense of unraveling around the standing and career of one of the most storied American celebrities, who is scheduled to perform stand-up at a theatre in Melbourne, Florida, on Friday night.

The Maxwell C King Center for the Performing Arts said this week it would go ahead with the sold-out show on the grounds that “while we are aware of the allegations reported in the press, we are only in a position to judge him based on his career as an entertainer and humanitarian”.

Others have proven to be less robust in the face of a barreling storm around the resurfaced allegations of rape and sexual assault. On Wednesday, NBC pulled the plug on a planned sitcom, earmarked for next year. Netflix has cancelled a one-off tribute to mark the star’s 77th birthday.

Cosby has never been criminally charged for any sexual offence. In a statement posted earlier this week, his lawyer responded to the accusations, saying the star did not “intend to dignify these allegations with any comment”. The statement described the claims as “decade-old discredited allegations”.

Serignese, told WPTV she was one of 13 anonymous women, listed as “Jane Does”, who were prepared to give evidence in the civil lawsuit brought by Andrea Constand in 2005. Constand, who alleged that she had been drugged and molested by Cosby the previous year, eventually settled with him for an undisclosed amount. The women never testified.

Serignese spoke of the distress of what she alleged had happened and how it still affected her 38 years later: “It’s always going to make me feel teary-eyed; the pain never goes away. The betrayal of my trust.”

She spoke openly about the racial factor in the abuse she alleged she suffered, as a white woman at the hands of a black man. “There was not a lot of inter-racial dating,” she said. “I came from Dearborn, Michigan. He was black, I was white, and he was married. It was not in my wildest dreams that that would occur.”

Serignese said that she contacted Cosby almost 20 years after the alleged incident, after she had moved to Florida and was in financial difficulties. He gave her $15,000 in two lump sums, she said.

People had asked her why she didn’t report to the police immediately, she said. “In 1976, that was a shameful thing to occur to a girl. You did not report that. They would victimize you, they would blame you, they would accuse you. Nothing would happen to that person.”