What have other people said about the incident?
Ford's lawyers said it was still unclear as of Sunday who will ask questions, as Republicans were trying to hire an outside female counsel for the role.
The judge has denied both allegations, labelling the latest "a smear".
Kavanaugh has denied the latest claim, saying the alleged incident "did not happen".
In a statement provided by the White House, he said the event "did not happen" and that the allegation was "a smear, plain and simple".
Eshoo said she met with Ford at her district office "for about an hour and a half" over the summer while Ford described her alleged encounter with Kavanaugh in the early 1980s.
The agreement sets the stage for a dramatic showdown as Kavanaugh and Ford each tell their side of the story. "It's also unremarkable that Ms. Keyser does not remember attending a specific gathering 30 years ago at which nothing of effect happened to her. Dr. Ford, of course, will never forget this gathering because of what happened to her there".
Keyser is the third individual to contradict Ford's claim they were present at the party where the alleged sexual assault occurred.
She had been considering speaking to the magazine for at least a week. "What in the hell did she have to gain by doing this?"
Judge Brett Kavanaugh is pictured answering questions during the second day of his Supreme Court confirmation hearing on Capitol Hill. She pushed him away, touching his penis in the process, she said. Many believed that somewhere, somehow, leftists would find someone else to come forward with accusations of sexual misconduct against Judge Kavanaugh.
The president's comments infuriated Democrats, dismayed many Republicans and risked further alienating women voters ahead of the November 6 mid-term elections, in which Democrats have a chance to win control of the House and perhaps the Senate. "A woman's experience should never be valued less than a man's career".
Senator Dianne Feinstein, the ranking Democrat on the committee, called for the "immediate postponement of any further proceedings" relating to Mr Kavanaugh's nomination in an letter sent to the committee's Republican chairman on Sunday evening. Taylor Foy, a Judiciary spokesman, complained that Democrats "actively withheld information" from the Republicans.
The make-up of the nine-judge Supreme Court is crucial, as it has the final say on often highly contentious laws. "Keep the faith, don't get rattled by any of this". "I don't think it was just 'Brett.' And I remember hearing and being mortified that this was out there". "And I hope that that will be the case, and that her courage is appreciated as well". But an anonymous classmate who did not attend the party told the New Yorker he's sure he was told about the incident at the time.
Mr Grassley's staff also agreed to let Ms Ford testify without Mr Kavanaugh in the room, for there to be only one camera in the room, "adequate" breaks and a high security presence. Ramirez was chosen repeatedly, she said, and quickly became inebriated. "I remain committed to defending my integrity". Charles Grassley, the top Republican on the Senate Judiciary Committee, said Grassley learned of the second woman's account when it was published in the New Yorker. Republicans narrowly control the Senate.