Now 73, Mr. Trump might not even be interested in running again if he were ousted by a Senate dominated by members of his own party. But for a president who is always spoiling for a fight, it might be sweet payback to be re-elected by voters after Democratic and Republican lawmakers banded together to give him the boot.

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At least one constitutional expert said that given the nature of the allegations against Mr. Trump — that he abused his power to enlist foreign help in next year’s election — disqualifying him would be an illogical penalty.

“If the impeachment is based on the Ukraine phone call and activity around that, and the idea is that he is improperly using his office to get dirt on his opponent, the remedy to that is to remove him from office,” said Edward B. Foley, an election law authority and constitutional law professor at the Ohio State University’s Moritz College of Law. “If the fear is the incumbent can’t fight a fair fight, then disable the candidate’s ability to not wage a fair fight.”

Of the eight federal judges who have been removed from the bench for crimes or misconduct, just three were disqualified from future office. The most notable person who was not barred was Representative Alcee Hastings, Democrat of Florida. Mr. Hastings, a former federal district judge, was tossed out by the Senate in 1989 on bribery accusations despite being acquitted in a criminal trial, only to be elected in 1992 to the House, where he still serves. (Some scholars argue that an ousted federal officer could not be barred from running for Congress in any event.)

The case of Mr. Hastings was a cautionary tale for congressional officials handling the impeachment in 2010 of Judge G. Thomas Porteous Jr. of Louisiana on bribery and perjury charges. They made sure to not only convict and remove the judge, but to disqualify him as well.

Yet disqualification remained something of an afterthought, and the Senate nearly missed its chance to do so. After the vote to convict Mr. Porteous, which automatically carries the penalty of removal from office, senators raced for the exits amid confusion over whether a second vote was needed on the future ban. It turned out one was, and senators were called back to cast a hasty vote of disqualification, which passed 94 to 2.

That overwhelming margin was not needed. The Senate has concluded, based on its own precedents, that disqualification can be done with a simple majority. The Constitution explicitly requires a two-thirds vote for conviction, but does not specify the margin needed for disqualification, so parliamentarians have ruled that the default for Senate votes is sufficient.