The last third party to survive is the Republican party. Its one of them things wherein there were actually politicians who had grown a couple and a spine to boot.
We have a 2 party system. 3rd parties have been tried, time and time again. There are several right now, Green, Libertarian, Socialist, Communist, etc. All failed, basically because they are endeavors of extremist groups that, in the end, don't get the support of the middle.
What 3rd parties really do well is to suck votes away from the established parties in elections. There are some, for instance, that blame suck for Hillary's loss. In the current political system a third party would, absolutely, guarantee another Trump term.
In the current environment the Dems are the most likely to spawn a 3rd party effort as there are little groups of true believers who seemingly can't stand the idea of giving an inch on ANYTHING. From my viewpoint these folks are very like the current Republican party and its a shame.