There are 2 parties in the USA today. If you cast your vote anywhere else, you are farting in the wind.
Well, occasionally not. The people who voted for Ralph Nader in Florida in 2000 put Bush Jr into the White House.
Otherwise, there is no room for anything else.
I could see a chunk of Republicans slicing off into a (true or false) Libertarian Party (maybe it would take one of each), a hard-core bible-thumping collection of arch social-conservatives, a dis-attached wealthy class concerned only with preserving their riches by any means necessary, and perhaps a remaining core of "Goldwater" Republicans that really do favor lower taxes but a massive military.
Democrats could have their own Libertarians of a "kinder and gentler" social attitude, a religious wing that took "love your brother" seriously, an amoral intellectual elite, and perhaps a European-style social welfare contingent.
But if any of these groups split off one at a time, they would be instantly squashed and made irrelevant. So we are stuck with 2 dysfunctional parties comprising wildly disparate collections of mis-matched bedfellows.
It would be amusing if it weren't so horrible.