As they brace for a high-stakes hearing with Supreme Court nominee Brett Kavanaugh and a woman who has accused him of sexual assault, Senate Republicans found themselves juggling the allegations of yet another accuser, the third woman to come forward so far about inappropriate behavior by the judge when he was a young man.

Judiciary Committee Republicans are pushing to get a staff interview with the latest accuser, Julie Swetnick, who is being represented by bombastic attorney Michael Avenatti.

“Our staff is extending an invitation to Mr. Avenatti today to produce his client today so that our staff can take a statement, and under the law that statement is sworn under penalty of perjury and penalty of going to jail. We did the same thing with Dr. Ford, we did the same thing with Ms. Ramirez,” Sen. John Kennedy (R-LA), a member of the committee, told reporters as he exited a Senate GOP luncheon Wednesday afternoon.

GOP senators, grim and hustling away from reporters after an unusually long Senate lunch, were tight-lipped about next steps for Kavanaugh. There were signs that some who had been dismissive of the original accusation were taking a more careful approach as the accusations mounted.

“Committee investigators have already reached out to Mr. Avenatti to ask for an interview from this person bringing the latest allegations and we’ll await the results of that investigation,” Sen. Ted Cruz (R-TX) said.

Avenatti’s client, Julie Swetnick, issued a sworn statement on Wednesday with serious allegations against Kavanaugh — detailed here. She is the third woman to come forward to accuse Kavanaugh of sexual misconduct.

Judiciary Chairman Chuck Grassley (R-IA) stressed that this was part of the process they have tried to use with everyone who has come forward with information about Kavanaugh.

He said the investigation into Swetnick’s allegations is “started right now,” when asked if such an investigation could be finished before the committee is scheduled to vote on Kavanaugh’s nomination on Friday.

Kennedy, Cruz and others said the potentially crucial hearing with Kavanaugh and Ford, the first woman to accuse Kavanaugh, will go forward on Thursday. But the rest of the schedule is unclear — including Republicans’ hopes to push Kennedy through a committee vote on Friday.

“I don’t know,” Kennedy said when asked by TPM if the Judiciary Committee would still hold that vote as scheduled.

When TPM asked Sen. John Cornyn (R-TX), a member of GOP leadership who’s on the committee, whether he supported holding a committee vote before hearing back from Swetnick, his reply was that “She may or may not accept our invitation for an interview.”

When asked if there’d be a vote on Friday, he was less than definitive.

“That’s the schedule,” Cornyn said.

Later Wednesday, Cornyn was also asked by TPM if there was enough time before Friday to get sworn testimony from Swetnick.

“Well certainly by the time the Senate votes on Tuesday,” he said.

Republicans emerged from a lunch caucus meeting with Vice President Mike Pence mostly trying to avoid commenting on the latest round of allegations.

“I am not going to make any further comments on the nomination until the hearing tomorrow,” Sen. Marco Rubio (R-FL) said, referring to the committee hearing where Christine Blasey Ford, the first woman to come forward with sexual misconduct allegations against Kavanaugh, along with, the Supreme Court nominee.

Asked if he was undecided on supporting the judge, Rubio said, “Like anybody else, I am going to watch the hearing tomorrow,” while also deferring questions about the appropriateness of a floor vote on Kavanaugh early next week.

Sen. Bob Corker (R-TN) said that he expected “at least 20 other Republican senators” who, like him, would be watching the hearing Thursday.

Members of leadership team denied that the latest allegations was causing divisions among the Republican caucus about supporting Kavanaugh

“Everybody in that room knows Kavanaugh and I think is impressed by him. They don’t know any of these other people,” Sen. Roy Blunt (R-MO) said.

Sen. John Thune (SD), the No. 3 Senate Republican, was asked if there was any wavering among the caucus on confirming the judge.

“Um,” he said, pausing three seconds, “no.”