https://en.wikipedia.org/wiki/Duverger%27s_law
> political systems with single-member districts and the plurality voting system, as in, for example, the United States, two main parties tend to emerge. In this case, votes for minor parties can potentially be regarded as splitting votes away from the most similar major party
If a third party grows it will either shrink again as voters realize they are splitting their vote against their biggest common opponent, or the third party replaces one of the two existing parties. Either way, you get two main parties.
I don't normally "this" a comment, but "this"!
The most effective single thing to promote a multiparty system is to switch to ranked-choice or approval voting (if staying with single-member districts) or to switch to multi-member districts with some kind of proportional representation. That would be where, say, everyone in Texas votes for their preferred party, and the 34 seats get allocated proportionally to party results.
Honestly, implementing Ranked Choice is the best compromise.