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 this 'rough draft' suggestion, House members would vote for four leaders of each "corner of the room." Four camps. With some sort of quasi-run-off voting method, members would vote until only four designated representatives remained. Those four would be the leaders of the four groups. Certain powers bestowed on each leader and group would make it of valuable interest for participation in dividing into four groups based on ideology.