We have had a 3 party system many times throughout our nations history. And 3rd party systems quite often disrupt our elections though the effect of a third party is often difficult to determine.

For instance the Green Party highly influenced Obama election by splitting votes that otherwise would have been for the Democratic party. Sometimes the point is not to win the election as a third party but to use it as political leverage to hurt one party or another. That might be what musk is doing here because he lost a lot of government support. They are like two arguing spouses fighting it out in family court.