Well, I commented on the subject a while back. I can imagine in the ruins of the former CSA, there could arise from some far-right demagogic figure who tries to challenge the people rebuilding America. Some Neo-Nazis, some CV remnants, some Neo-Rumsfeldians.
But realistically, such a group would not last very long if hunted by a professional army.
As I've said earlier, rebel/extremists groups only really succeed if they have, like foreign backing from a major power, or access to valuable mineral.
OTL, ISIS and the militias tearing apart the Eastern Congo have access to valuable oil and minerals. Mao OTL was only able to take over mainland China with Soviet backing.
These Neo-Nazi type groups might be able to be headache to whatever force is trying to rebuild the former CSA, but without some kind of foreign backing, they won't last long. They won't really be able to do much in the smoky ruins of the American hinterland. And I doubt the occupation force, having faced one far-right extremism, will ever tolerate another.
Like I said, the theme of this story for me is the systematic learning of the specific wrong lesson that will cause the most suffering. The occupation force will grow exhausted with the constant disorder and possibly disillusioned by their mandate, depending on just how heinously punitive it is. They'll bug out and create a vaccum that will invariably be filled by the worst possible replacement.
That doesn't mean multiparty democracy is over. Rumsfeldians will remain a fringe, but other parties can still thrive.
Other parties could become Rumsfeldian. Like I keep saying, wrong lesson that makes things worse is the recurring motif here.
Agnew thought he could escape impeachment by pardoning himself? Wrong, made things worse.
His chief of staff saw what happened, and concluded that Agnew was not corrupt/ruthless enough? Wrong, made things worse.
George Wallace thought tearing down the party system to make an opening for himself would make the country better? Wrong, made things worse.
Democrats respond to the failures of the 70's and the success of Rumsfeld and decide to accommodate the latter and move to the right? Wrong, made things worse.
Libertarians and WTP, disillusioned by the major parties, think they can fix things by splitting off and going their own way? Wrong, made things worse.
Rumsfeld, having been betrayed by too many Republicans, decides to lean on CV for support, thinking they're more simple-minded and easily led. Wrong, made things worse. His former corporate allies make the same mistake again later, having also learned the exact wrong lessons from his impeachment.
Responding to Rumsfeldia by outlawing opposition parties would be taking the wrong lesson from it, and make things worse. Which is to say, it is perfectly in keeping with what we've seen so far.
Other thought - there will absolutely be some analogue to Anti-Japaneseism for America in this story. The absolute worst case scenario I can think of would involve Jack Kevorkian becoming President on a platform of self-genocide. The idea would be that not only did American government fail, but America, built on slaves and stolen land as it is, is inherently immoral and could have ended no other way. There are few to no Native Americans left, so the only recourse is self-destruction and letting nature reclaim its defiled territory. The world looks on in utter disbelief as, in a spectacle that makes Coe's wildest designs look tame, an entire nation marches willingly into its own gas chambers, utterly broken and unwilling to bear existence in this accursed universe any longer. That would be too grimdark even for this timeline. Anything less than that is still in the running, I think.