Weinstein, 72, wants the extra charge thrown out, arguing through lawyers that Manhattan prosecutors only brought it to bolster their case with a third accuser after New York's highest court overturned his 2020 conviction on rape and sexual assault charges involving two women.
Judge Curtis Farber is expected to rule on that and other matters, including the trial date - a task that's been complicated by an increasingly crowded court calendar.
Weinstein's lawyer, Arthur Aidala, is representing conservative strategist Steve Bannon in a border wall fraud trial that's set to start on March 4 before a different Manhattan judge. Meanwhile, Farber has a murder trial in March.
Before Bannon's trial date was set last week, Aidala had suggested that Weinstein's trial go first in "the interest of humanity," citing the ex-studio boss' declining health.
Weinstein is being treated for numerous medical conditions, including chronic myeloid leukaemia and diabetes.
"They know that Mr Weinstein is dying of cancer and is an innocent man right now in the state of New York," Aidala argued in court last week. He pleaded to prosecutors: "Can I try this dying man's case first?"
Weinstein is being retried on charges that he forcibly performed oral sex on a movie and TV production assistant in 2006 and raped an aspiring actor in 2013. The additional charge, filed last September, alleges he forced oral sex on a different woman at a Manhattan hotel in 2006.
The Manhattan district attorney's office said in court papers the woman, who has not been identified publicly, came forward to prosecutors just days before the start of Weinstein's first trial but was not part of that case.
Prosecutors said they did not pursue the women's allegations after Weinstein was convicted and sentenced to 23 years in prison, but they revisited them and secured a new indictment after the state's Court of Appeals threw out his conviction last April.
Farber ruled in October to combine the new indictment and existing charges into one trial.
Weinstein co-founded the film and television production companies Miramax and The Weinstein Company and was once one of the most powerful people in Hollywood, having produced films such as Pulp Fiction and The Crying Game.
In 2017, he became the most prominent villain of the #MeToo movement, which erupted when women began going public with accounts of his behaviour.
He has long maintained that any sexual activity was consensual.
Weinstein has remained in custody in New York's Rikers Island jail complex, with occasional trips to a hospital for medical treatment, while awaiting the retrial.
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
