Actually, nobody “runs for president. Each candidate has a slate of Electors in each state pledged to them. Any intent to directly violate the 22nd Amendment would therefor require “framing timbers” to be erected aforethought in each state he needed for an EC victory. And even then, any such elector would individually be violating the Constitution, and no one who had the slightest respect for the Constitution would count votes for a third-termer as legitimate.A third-termer would do just as well to call off the election altogether as to try to win an election. People prattled about a “Constitutional crisis” during the winding down of the Nixon Administration, but it was never that. It would only be a constitutional crisis if the president had been impeached and convicted and refused to leave office. Which no one seriously proposed was in the offing.