That is, in theory, a good idea. But for a third party to play a meaningful role, the first thing that would have to change is that first-past-the-post had to be abandoned. Else, all the effort you take to establish a third power will be void soon, history shows that a potential third power immediately results in one of the former two powers becoming irrelevant quickly and the power you established replacing it, resulting in a new, but by no means different, two party system.
The only ones that could change the system itself are, though, exactly the same entities that have no interest at all in changing it. If there is one thing that two parties in a FPTP system agree on, independent of possible differences, is that the system is great. Because it does exactly what is in their interest, ensure that they have only one potential competitor instead of many. And eventually the two competitors become so similar (for the simple reason that they want to appeal to as many voters as possible, I can get into detail but I guess it's self explanatory why the two parties become very similar over time) that it doesn't really matter which one you support.
The system ensures that you have two near identical groups to choose from and both of them have no interest in changing the election system to one that allows more variety in the political landscape.
The main reason that it works for most of Europe is that few countries in Europe actually have a first-past-the-post system in place. Coalitions are very common in most European countries, with parties needing usually between 3 and 6 percent of the votes to make it into parliament. And it's far from impossible that such comparably small parties can become part of the government if a big party needs just a few more seats to get a working majority. That's why the Greens actually made it into governments in Europe.
And now tell me how this should possibly happen in the US.