Since the one party (a.k.a. "two party" system) of the US is a problem, efforts to encourage diversity is a solution. So here's the plan: Instead of ignoring the existence of political parties on the Constitutional level, officially acknowledging a minimum of four so to at least double the ideological representation, and move beyond the 1 dimensional left - right spectrum.
In my 'rough draft' suggestion, House members would vote for four leaders of each "corner of the room" or four camps. With a quasi-run-off voting method, members would vote until only four designated representatives remained. Those four would be "leaders" of some sort with certain powers that would make it of valuable interest for participation and delineation of the complexity of thinking representing a large populace.