Yea but those third parties are a joke. And of course there is the "Catch 22" of thier existance - they have no power and no responsibilities and no decisions to make and nobody to be accountable to. The second any of those third parties got power they would start playing the game with whatever interst groups were around at the time whether they be unions or business, same thing really - union is basically a corporation that sells value added labor services - so it's all the same. Of course there are also seniors groups, environmentalists, political activist groups, religious groups and so on and so on...
Frankly any government or administation regardless of party alignment will have to deal with these interst groups because in the end these intrest groups do represent segments of the population with viable and yes, often competing concerns - otherwise it would be a dictatorship.