The university said Monday that the school's Board of Governors would meet Thursday to discuss hiring an adviser to report on what went wrong with Mike Rice.
University President Robert Barchi said that employees are going through video of practice sessions from other sports to see if any other troubling behavior needs to be rooted out.
The scandal has had far-reaching implications on the university's athletic department.
Rice was fired on April 3, a day after a video of him at practice was made public. Athletic Director Tim Pernetti later resigned, as did an assistant basketball coach and the university's top in-house lawyer.
On Monday, the university chose former dean Carl Kirschner to serve as acting athletic director while a search is conducted for someone to fill the job permanently.
There's been widespread anger over the video, which was presented to university officials in November by a former basketball program employee who last week sued the university, claiming he was let go because he was a whistle-blower. A person with knowledge of the situation by who requested anonymity because the investigation has not been made public, has told The Associated Press that the FBI is looking into whether the ex-employee, Eric Murdock, unlawfully asked for money in exchange for not making the video public.
Gov. Chris Christie said at a news conference Monday that Rice needed to be fired promptly and that his antics cost him credibility with athletes and their families.
"What parent would let this animal back into their living room to try to recruit their son after this video?" he asked.
Christie also said that he wants to know why Rice was not fired even before the university knew about the video of his behavior at practice.
That's a question that the investigation being commissioned by the university could look at.
Questions of who knew what about Rice's behavior and when, and what they did about it, are likely to loom large as the investigations continue.
On Monday, Christie said anyone who knew about the behavior previously and did not act to oust Rice was in the wrong. He criticized the reaction of those who knew about it and did not fire the coach months ago, when the video was given to university officials and viewed by - at least - Pernetti, university interim counsel John Wolf and Chairman Mark Hershhorn of the university Board of Governors' athletics committee.
In a statement released by his lawyer late Monday, Hershhorn said he did call for Rice's firing on the day in early December that he watched the video. He said he told Pernetti that if the video was authenticated, Rice needed to be immediately terminated. Contrary to his recommendation, Hershhorn said, the university chose to discipline Rice instead of let him go.
The Rutgers administration would not comment on Hershhorn's account of events.
Meanwhile, a group of five Democratic members of the state Assembly made a half-dozen requests for information from Rutgers Monday under the state's Open Public Records Act. The lawmakers, who plan to hold hearings on the situation, asked for communications about Rice's hiring in 2010, his firing this month and several issues in between.
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Mulvihill reported from Haddonfield. Also contributing were Associated Press reporters Angela Delli Santi, Tom Canavan and Tim Sullivan.
