The White House said Tuesday it would be "open" to allow Senate testimony from a second woman who accuses Supreme Court nominee Brett Kavanaugh of sexual misconduct.

"Certainly we would be open to that, and that process could take place on Thursday," White House press secretary Sarah Huckabee Sanders said on ABC News' "Good Morning America."

President Donald Trump has been clear, Sanders said: "Let them speak, but let's also let Brett Kavanaugh speak, and let's let him tell his side of the story before we allow allegations to determine his entire future."

The White House's stance appears to clash with the lines drawn around the Senate hearing by Judiciary Committee Chairman Sen. Chuck Grassley, R-Iowa, who limited the hearing to two witnesses. Senators are currently scheduled to hear from Kavanaugh and Christine Blasey Ford, who has accused him of sexually assaulting her when they were teenagers.

The second woman, Deborah Ramirez, has alleged that Kavanaugh's sexual misconduct came during a party at Yale University in the 1980s, when they were classmates. In a story published Sunday by The New Yorker, Ramirez claims Kavanaugh "exposed himself" to her, and caused her to touch his genitals "without her consent as she pushed him away."

Kavanaugh has strongly denied both allegations, and in a Fox News interview that aired Monday evening, he reaffirmed his commitment to pursue a seat on the high court.

Grassley has not shown any indication in recent days that he plans to allow more witnesses to testify, as many Democrats have called for. Grassley's office did not immediately respond to CNBC's request for comment on Sanders' remarks.

Grassley has also resisted Democrats' calls for an FBI investigation into Ford's allegations against Kavanaugh. Ramirez said she believes a federal probe of her own allegation "would be warranted."

Sanders backed Grassley's refusal to bring in the FBI to investigate the claims against Kavanaugh. "We have a process in place," she said.