This is important so it deserves many more comments: it's not a two party system, it's a first past the post system. So long as we continue to use an inferior, outdated voting system, having two dominant parties is inevitable. Talking about overthrowing the two party system is pointless and misguided; it's a red herring.
It's troublesome both at the grand strategic level with FPTP and Duvuger's Law and such systematic issues, but also at the local tactical level. Ballot access laws are written by the two major parties and often designed in a way to thwart third party ambitions, probably fear of competition that could drive the spoiler effect. This extends to everything from higher signature requirements to get on ballots all the way to requiring an impossibly high percentage of the vote to qualify for FEC primary matching funds, let alone being invited to the presidential debates.