In August, CBS hired two law firms to investigate allegations of sexual assault and unwanted advances following a New Yorker report that featured claims against Moonves from six women spanning different periods over two decades, from 1985 to 2006.
The new claims detailed in the New Yorker include that Moonves physically exposed himself to women without their consent, and forced women to perform oral sex on him.
Griffin also tweeted about the matter, responding to Hollywood Reporter editorial director Matthew Belloni calling Moonves' impending exit the "end of an era". A spokesman for the board did not immediately return requests for comment.
The six women in the latest piece allege sexual harassment or assault by Mr Moonves between the 1980s and the first decade of this century. Golden-Gottlieb didn't report the assaults until a year ago but prosecutors declined to press charges because the statute of limitations ran out. CBS has spent much of his tenure as the nation's most popular broadcast network, with hits like "The Big Bang Theory" and "NCIS", and its success has made Moonves one of the highest-paid and most powerful executives in the business.
Mr Moonves, 68, denies the allegations, calling the latest "appalling".
CBS' CEO Les Moonves is in the process of negotiating his exit package worth up to $100 million after allegations of sexual misconduct.
Among the new accusers is Phyllis Golden-Gottlieb, a now-retired TV executive who once worked at the Lorimar production company with Moonves.
Moonves, in a statement to the New Yorker, acknowledged three of the encounters while maintaining that they were consensual. "In my 40 years of work, I have never before heard of such disturbing accusations", Moonves said.
Seven years after the incident, Moonves was reportedly "furious" and "aggressive" in tone to several sources after Jackson signed a book deal with Simon & Schuster (which is owned by Viacom) for her 2011 memoir "True You".
He said on CNN that "these women are coming out now" because "they have been extraordinarily frustrated by what they perceive to be inaction on the part of CBS and its board. They felt this was a board that has let a powerful man who makes a lot of money for this company, in the words of one person, 'get away with it'".
Time's Up released a statement slamming CBS for a "culture of toxic complicity" at the company, and insisted that it will "accept nothing less than full transparency of the investigation's findings, a commitment to real change across all levels of CBS management and no reward for Les Moonves".