The biggest problem with a two party system like the US has is that it simply doesn't allow for the full spectrum of the way people think. "Left" and "right" try to harness both an economic scale and a personal liberty scale into one. On the left, you want government involved in commerce (usually for protectionist and wealth redistribution reasons), along with letting everybody personally do what they'd like, make love how they'd like, have abortions, etc.. On the right, of course, you want no regulation of business, since "unfettered capitalism" is a kind of god, but you want people to all do the same sort of things in the same sort of ways, whether it's comfortable for them or not.
My political view turns that into a quadrant, left and right, up and down. On the left, I do want government to have some involvement in regulating business, if only to make rules about cheating, false advertising, monopoly avoidance, regulations regarding assets required to back and protect credit, and that sort of thing. So on the left right scale (-10 to +10) I'm about a -3. In terms of personal liberty (authoritarian at the top or plus side, libertarian at the bottom), well, I don't think the state has much business in my private life, even if I do decide I want to marry another man and allow others to make similar choices for themselves, again, I'm about a -3, because I still think we humans need some rules to live by.
Anybody who understands what I just wrote, will not be surprised to learn that here in Canada, I have, over the years, voted for 4 political parties. And so long as I'm able and enfranchised, will likely to continue doing that, based on the party's platforms, leadership, and who's running in my local.
Y'all should try it!