Banning parties would be easy, you can’t ban alliances, but the party system is easy to break apart. First step: no mention of any level of affiliation on any ballots ever, no R candidates, no D candidates, just candidates. Then you get rid of all that majority-minority stuff on the Congressional floor. Third change the primary system from one that makes party nominees to one that picks the 3 candidates with the most support (basically like the NASCAR Cup). Those three steps right there would take away most of the power political parties have, sure politicians could still form alliances, and they could be large alliances, but those alliances wouldn’t be built into the structure of the system. That’s a big part of the problem right, because 2 parties are built into the basic foundation of the system anybody trying to come at politics from outside those 2 parties is immediately on the margin even if they somehow win.
That's how they do it in Europe.
Most Americans have no idea what goes on in European parliamentary politics and you'd have a hard sell.