Nebraska

Not in any appreciable manner. Most of the legislation is for the individual candidate not their party or lack thereof, however first pass the post devolves to a two party system by it's very nature. Add the Electoral college and the fact that primaries are run by the Political parties themselves, states run the elections with little to no federal standardization in voting and you get the current mess the US is in.

https://medium.com/@odtorson/on-electoral-colleges-first-past-the-post-and-the-will-of-the-people-3a9d31379b9

This isn't considering the influence money/corporations/billionaires have with SuperPACs nor the vote suppression. The cluster is sufficiently fucked.

https://www.brennancenter.org/our-work/analysis-opinion/moneys-control-over-politics-has-never-been-greater

https://www.aclu.org/news/civil-liberties/block-the-vote-voter-suppression-in-2020