More than a third party, I'd like to see more of an independence movement. Seriously, I don't think the majority of Americans should belong to a political party, but rather stay independent. The idea would be to make the political parties work for your vote, instead of presuming you will vote for them.
You should only belong to a party if you believe in every single issue on that parties platform. Otherwise, you should stay independent, and then vote for the candidate that most closely represents your view, or whatever criteria you think you want in a representative.
Heck, at this point, I'd be happy with a sizeable minority of active independent voters.... enough to keep the major parties honest.