Such committees can accept donations of up to $5,000 per donor per year — far less than the donation limits for the committees formed by Mr. Trump’s campaign and the Republican National Committee — but a leadership PAC could accept donations from an unlimited number of people. It could also accept donations from other political action committees.

A leadership PAC could spend an unlimited amount in so-called independent expenditures to benefit other candidates, as well as fund travel, polling and consultants. Mostly, it would almost certainly be a vehicle by which Mr. Trump could retain influence in a party that has been remade largely in his image over the past four years…

Still, a PAC could give the president an off-ramp after a bruising election fight, as well as keep him as a dominant figure as the next Republican presidential primary races are beginning for a new standard-bearer.

“President Trump is not going anywhere anytime soon,” said Matt Gorman, a Republican strategist. “He’s going to insert himself in the national debate in a way that’s unlike any of his predecessors.”