How you vote isn’t going to impact the two party system, because there’s still only two realistic outcomes. Democrats win or Republicans win. Withhold a vote from one party and you empower the other party.

Not to mention, our third parties actually maintain the two party system. They don’t oppose it. They criticize mainstream politicians for corruptions and then go rub shoulders with Russian oligarchs. They have no intent to actually win, it’s just a grift. If they were serious about becoming a player, they would have invested in a 50 state strategy to build up a local presence everywhere. And then from a solid base, gradually win elections and climb up the ladder. Instead, they waste all their money on the presidential election and hope you don’t realize that if they do win, they have no representatives in Congress.

Realistically, ending the two party system as a new party within that system is unlikely. You’d need to massively build up local. Instead, we’re better off co-opting the parties. Do what the Tea Party did and hijack the party to go where you want.