Not that it has any chance of passing in the current Congress, but if there is a major shift following the next election, who knows? Senate Majority Leader Chuck Schumer has proposed what he delightfully calls the No Kings Act, the putative purpose of which is to reverse the Supreme Court’s presidential criminal immunity ruling in Trump v. US and strip the president (and vice president, although the Court never mentioned the Veep) of any immunity from prosecution whatsoever.
(1) NO IMMUNITY.—A President, former President, Vice President, or former Vice President shall not be entitled to any form of immunity (whether absolute, presumptive, or otherwise) from criminal prosecution for alleged violations of the criminal laws of the United States unless specified by Congress.

