Can you explain more about this coup?
Until the 12th Amendment was passed electors voted twice, they couldn't vote for the same person twice, and whoever got the most EV's became President, runner up Vice-President. But in 1800 the Democratic-Republicans hit a snag, both Jefferson and Burr had 73 votes, someone was supposed to throw their Burr vote elsewhere to make him VP, but they didn't. So the election was thrown to the House where Federalists keep deadlocking to embarrass Jefferson. Aaron Burr even tried to convince some of them to vote for him, make him President, and stage a coup on Jefferson who everyone intended to be President.
In comes Alexander Hamilton, rival of Jefferson, hateful foe of fellow New Yorker Burr. He convinced the House to vote in Jefferson as he respected him more the Burr, a man who he considered to have no morals. The 12th Amendment was ratified 1804, by then Burr was pariah for killing Hamilton in a duel, and was dumped off for New York Governor George Clinton.
Emperor Julian proposes that if all was the same in 1800, but with Clinton as the other half of Jefferson's ticket, Hamilton would back Clinton (who he hated not as much as Burr), steal the Presidency from Jefferson, and force Jefferson to try and stage a counter-coup to take the Presidency. An interesting idea, but unlikely because I believe Hamilton also hated Clinton for all the effort the Pharaoh of New York put into slandering the Constitution and Hamilton.