While there are always more than two positions you can hold on a subject, most of those positions can be simplified into two directions. Having a two-party system allows for a political tug of war, where over time the will of the people can (in theory) pull public policy towards their interests.

In a multi-party system, the general ideologies most subscribed to have the most parties. Take Canada for example, more than half the population considers themselves left-of-center. So much so, that there is so much variation between these leftists that there is two left-of-center parties: the Liberal Party (center-left) & the New Democrat Party (far left). There is only one right-of-center party: the Conservative Party.

Many of those leftists would accept either the Liberals or the NDP. Because of this, both left-of-center parties have to fight for those people's votes. The number of people who would consider both the Conservatives and the Liberals are much less since, in most elections, anyone right-of-center defaults to the right-of-center party.

This often splits the left-of-center voters (a statistical majority), and results in the only right-wing party getting closer to a majority of the Seats (Electoral College electors). So changing the two-party system can not be the single biggest aspect that you change, since you would also have to overthrow the entire election system to avoid false majorities. Firstly, both the Electoral College and the First Past the Post systems would have to change in elections. Secondly, US govt is set up in a way where parties dont exactly work with each other. You would also have to change that, so if you have say 60% of the govt being leftist parties, they can work together to create generally leftist policies.