Ramirez is cited by the New Yorker as saying Kavanaugh exposed himself to her during a drunken dormitory party.
With Kavanaugh's confirmation prospects already hanging the balance, the news of a second set of allegations is likely to alarm Republicans who are hoping to push Kavanaugh's nomination through the Senate, where they hold a slim 51-49 majority.
Kavanaugh is scheduled to appear before the committee on Thursday to defend himself against an allegation of sexual assault against him by Palo Alto University professor Christine Blasey Ford. DN! speaks with Jodi Jacobson, president and editor-in-chief of Rewire. Kavanaugh denied the allegation.
The other male classmate Ramirez said was involved in the incident told the magazine, "I have zero recollection".
The second claim against Kavanaugh dates to the 1983-84 academic year, which was his first at Yale University.
At a White House ceremony revealing his choice, Trump describes Kavanaugh as a man of "impeccable credentials" and a "true thought-leader among his peers".
"The additional information provided by Ms. Ramirez regarding Kavanaugh's behavior in college presents a pattern of conduct that makes it absolutely clear that he is entirely unsuited to serve on the Supreme Court", Sen.
Dr Ford has agreed to testify before the Senate Judiciary Committee on Thursday.
A handful of senators in both parties remain undecided on Kavanaugh's nomination.
In a statement provided by the White House, Mr Kavanaugh said the event "did not happen" and that the allegation was "a smear, plain and simple".
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Meanwhile, Senate Democratic leader Chuck Schumer and Senate Committee on the Judiciary Ranking member Dianne Feinstein, in a letter, urged President Donald Trump to direct the Federal Bureau of Investigation to immediately and thoroughly investigate Ford's allegations and report to the Senate as soon as possible.
Ramirez alleged somebody said Kavanaugh's full name out loud immediately after the incident where he harassed her at Yale. Ramirez and her attorney could not be reached for comment on the record.
Avenatti, who has said he's considering a 2020 Democratic presidential bid, told the AP that he will disclose his client's identity in the coming days and that she is prepared to testify before the committee, as well as provide names of corroborating witnesses.
Proceeding with Kavanaugh seems to give Republicans their best shot at filling the Supreme Court vacancy - and giving the court an increasingly conservative tilt - before November's elections, when GOP Senate control is in play. Kavanaugh's nomination is now in question, and Republicans are trying to continue the confirmation process with seemingly little pause due to the accusations.
Grassley scraps the confirmation vote on Kavanaugh that the committee was scheduled to hold September 21 and says the panel will hold a hearing September 24 to hear from both Ford and Kavanaugh about the sexual assault allegations.
CNN has not independently confirmed The New Yorker's reporting. Brett Kavanaugh is an absolutely outstanding person.
Joining the maelstrom, Michael Avenatti, the attorney representing porn actress Stormy Daniels in her legal fight with President Donald Trump, claimed to represent a woman with information about high school-era parties attended by Kavanaugh and urged the Senate to investigate.
In the run-up to an appearance by Kavanaugh and his main accuser at a dramatic Senate Judiciary Committee hearing, Trump called the accusations "totally political" and among "the single most unfair, unjust things to happen to a candidate for anything".
Senate Judiciary Committee Chairman Chuck Grassley, R-Iowa, wrangled with Ford's lawyers for the past week over the exact terms of her appearance. They have protested the panel's treatment of Ford, comparing it to bullying.