“Can I change my vote?”

That was the question several motion picture academy members were asking after five women accused actor James Franco of inappropriate or sexually exploitative behavior in a Times investigation published Thursday.

The allegations — two of which showed up on Twitter last Sunday, the night Franco won a Golden Globe for his lead turn in “The Disaster Artist” — arrived just as the voting period for Oscar nominations was ending.

Franco, who denies the allegations, is considered a strong possibility for an Oscar nomination for playing Tommy Wiseau. Wiseau became a cult figure after the release of his 2003 film, “The Room,” which many critics call the worst movie ever made.

This year’s eight-day Oscar voting window ended Friday, and, according to several consultants, the heaviest voting days are the first and the last. Which means Franco could already have banked a number of early votes but lost late ones; the nominations will be announced Jan. 23.

Either way, Franco is a last-minute figure of controversy in an Oscar season rife with it. The fall of Harvey Weinstein, after stories in the New York Times and the New Yorker detailed multiple allegations of sexual harassment and misconduct, triggered an avalanche of accusations against a number of men that reshaped this year’s awards season. Weinstein was booted out of the academy, Kevin Spacey was erased from Oscar hopeful “All the Money in the World” and a handful of campaigns died in the planning stages.

Now, with Franco accused by five women of exploiting his position as a teacher and mentor, some academy members are rethinking their pick.

“I voted for him, and reading that story, I regret that I did,” said an actress who, like other academy members interviewed, spoke on the condition of anonymity. “The last thing we need, right in the middle of all this talk about sexual harassment and gender inequity in Hollywood, is someone like that as an Oscar nominee.”

Franco’s nomination will be decided solely by fellow members of the actors branch, which, with 1,218 active voters, is by far the largest group within the Academy of Motion Picture Arts and Sciences. Speaking to a sliver of that group, The Times found most inclined to distance themselves from Franco.

“I liked him in ‘The Disaster Artist,’ but I wish I could have that vote back,” said another actress. “We had the Casey Affleck thing last year. It detracts from what we should be doing — celebrating the work.”

Affleck won the lead actor Oscar in February for “Manchester by the Sea,” but his awards season was dogged by questions over two sexual harassment suits that were filed against him by two women in 2010 in civil court. Affleck, who settled the cases, denied the allegations.