How is it that we maintain a two party system?

America has a first past the post system where the winner takes all. There's no reward for a second place finish, much less third or fourth. As a result, coalitions of voters will form the largest parties possible in an effort to reach majority status. There's no incentive to maintain a smaller party.

As an alternative, we could copy other countries that have at-large delegates to the legislature based upon the percentage of the vote each party wins in a general election.

The two-party system doesn't really exist. We basically have a two-headed single party, and checks and balances are becoming nothing more than something that exist on paper only.

The U.S. Doesn't allow for run- off elections in the event that no candidate fails to reach the 50.1% threshold. If run-off elections were held between the top two candidates after an election where no one broke 50% you would see many more Green and Libertarian politicians, especially at local levels.