The thing is, if the central government retains any semblance of power, national parties are going to coopt the local parties for their own infrastructure. You can have multiple parties in Congress, even if vote-splitting makes it inefficient. You can't split the presidency. Coalitions work in parliamentary systems because the parliament is elected, and then the various parties negotiate with each other for who will form the coalition, making the needed concessions to buy off coalition partners. That doesn't really work with the presidency; coalitions need to be made before the election,* which means that in practice you will have groups of local parties that will always coalition together, and very soon, you end up with national parties again. Since the rump Republicans and Democrats will still likely be around, you probably even end up with those two being the national parties still.
It's what happened to the NPL and all the rest, historically. They are still around as state-level affiliates (so e.g. Barack Obama was on the ballot in ND as the "Democratic-NPL" candidate), but on a practical level are merely part of the larger party.
It's also worth mentioning that the big-tent nature of the two parties and the decentralized nature of the American government already makes the parties essentially coalitions. The Dixiecrat wing of the Democratic Party was the most famous example, but even today it is understood and acceptable for members of congress to buck their own party on matters of concern to their state. For example, Joe Manchin may be a Democrat, but as long as West Virginia's economy is centered around coal, he's not going to back serious climate change legislation.
You could certainly develop more of the state-level affiliated parties, but full-on independent parties won't really work outside of somewhere like Puerto Rico.
*I suppose you could work something out with the members of the electoral college doing the coalition forming, but that's so alien to the American political position as to require a much earlier POD. It's also undemocratic and opaque as can be.