MADISON, Wis. — A University of Wisconsin Madison student already accused of sexually assaulting a woman in his apartment after a date was charged Thursday with sexually assaulting three other women since early 2015.

Alec Cook, 20, of Edina, Minn., now faces seven counts of second-degree sexual assault, three counts of third-degree sexual assault, two counts of strangulation, two counts of false imprisonment, and one count of fourth-degree sexual assault.

The complaint that prosecutors filed Thursday accuses Cook of assaults dating back to March 2015. Prosecutors said one of the women was assaulted multiple times during a ballroom dancing class she was attending with Cook this past spring. The other alleged victims were a woman Cook met at a party at his apartment in March 2015 and another he met in a human sexuality class last February.

Cook was charged last week with sexually assaulting a woman in his apartment after inviting her to come home with him after studying in a campus library.

Media reports of those charges have driven dozens of women to report to police their encounters with Cook. Officers searching Cook’s apartment found a black book listing women he’d met and documenting his ‘‘sexual desires,’’ authorities said.

Dane County Circuit Court Commissioner Brian Asmus set Cook’s bail at $200,000.

His attorneys told reporters after the proceeding that they believe the ballroom assaults never happened, noting the complaint didn’t cite any witnesses.

The rest of the encounters, they said, were consensual.

Associated Press