What do you mean by “another presidency”? If he wants to build a replica Oval Office and pretend to be POTUS, no one is going to say anything, except that he’s delusional. If he tries to order around the DoD, or Homeland Security, they will presumably ignore him.
I don’t think just playing dress-up President is illegal, but at a certain point it gets there:
Whoever falsely assumes or pretends to be an officer or employee acting under the authority of the United States or any department, agency or officer thereof, and acts as such, or in such pretended character demands or obtains any money, paper, document, or thing of value, shall be fined under this title or imprisoned not more than three years, or both.
Speaking of Mar-a-Lago, what are the odds the town will enforce the “no living here” agreement signed by Trump. At least some residents are asking that he be held to it. Seems cut and dry but will he try to sue his way into having the prior agreement voided?
Well first you gather together your pretend electoral voters, then you submit your pretend electoral votes to the pretend president of the senate and have him certify them, then you have your pretend swearing-in ceremony before you head to the pretend whitehouse. Then you have your pretend news neworks cover it.
I do wonder if it would be within the legal authority of Homeland Security to instruct that the ExPOTUS protective detail will personally charge him for the expenses of any service at any appearance or during any activity in which he portends to usurp the authority of POTUS-in-office. Because you just know there will be a nonzero number of county clerks/Sherriffs/state assemblypeeps in wingnutland who will be eager to welcome him to make appearances and announcements not just as political candidates but while in official duty, and outright declaring it is him they recognize as rightful POTUS.
I think any illusions Trump has of running a shadow presidency will quickly shatter. Because Trump will be lacking an important asset after January 20; access to the federal budget. And it’s not like lobbyists and foreign governments have any interest in bribing a former president.
Trump brags about how rich he is. But his real wealth is probably nowhere near as large as he claims. If he tries to run a full administration on his own dime, he’ll soon be looking at bankruptcy number eight.