I assume that you guys have some version of proportional representation. The US doesn't. It would take a complete rewrite of the US constitution to get rid of the two party system.
Re-empowering electors could help with respect to presidential elections. Popular election of senators really ties our hands at the senate level, though. Point being, it is difficult to turn a plurality into a compromise majority without either a runoff or a delegated negotiation of some sort. Parliamentary systems have that baked in, of course.