Nope.
We have two major parties because of certain peculiarities of our electoral laws.
Electoral laws determine party systems. This is an axiom of political science.
Parliamentary systems use slates of candidates, and foster multi-party systems.
Our systems of proportional representation, election by plurality, and the Electoral College all steer our system to two major parties. It's always been thus.
First we had the Federalists and Republicans (later the called Democratic Republicans, then Democrats); then we had the Democratic Republicans and the Whigs; then we had the Democrats and Republicans.
In our 216 years of democracy, we've only had four major parties, and never more than two at once, spread out over three separate two-party systems.
Only two things can change the status quo: completely impossible Constitutional Amendments (too many states of low populations would have to willingly give up power), or the death of one of the existing major parties. Otherwise it's Democrats and Republicans as far as the eye can see, other than the occasional, unsustainable fluke.