Notably, we could do that while still abolishing first past the post. Requirements for holding a previous position could be added while simultaneously reforming the federal (and hopefully also state) systems to be compatible with multiple parties. I imagine it would be sufficient for each level to require a single term served at the previous level - city or county, state, and federal.

The downside is encouraging career politicians, but the upside is that if you can't win increasingly high stakes elections over a period of 10 years or so then you probably have no business being the president of a country this size.