Break the powers of the president into multiple different offices.

As long as we're talking esoteric political ideas, the big one here is to split head of state from head of government. It might not affect the function of government much, because the head of state is largely ceremonial in modern systems, but it's I think it's super-important psychologically.

A lot of (most?) people have trouble thinking about the office of the President as an abstract concept separately from the person of the President. Therefore, the President becomes an avatar of the United States, taken to be the living embodiment of our identity as a nation. That's why so many people freak out about "the destruction of America" when a member of the other party, with values they don't share, becomes the President, and it makes elections feel like a polarizing, existential referendum.

By contrast, King Charles is the head of state in the UK, while the head of government (the prime minister) comes and goes, and a stable avatar of the nation, largely above politics. They have their share of major problems over there, to be sure, but at least the nation has a shared identity to rally around when needed.