It's called "cumul de mandats" (accumulation of mandates). Severe limits have been put in place, and more are being added all the time, to put an end to that. Sometimes it's an actual law, sometimes it's just the principles a given administration puts in place, but cumul de mandats is frowned on more and more.
Yeah, twenty years ago when I was studying the French system it was noted that efforts were being made to curb it (thus my disclaimer). But it’s the French and only twenty years so I wasn’t sure if the needle had actually moved or not.
Wiki sez you can only do it in Connecticut, and then only with municipal offices. https://en.m.wikipedia.org/wiki/Dua...on places no,branch of the federal government.