They have implemented a type of a mixed state that has both socialist and capitalist parts
Personally, I find it very similar to corporatism.
I would describe the CCP political ideology as “authoritarianism” and the economic ideology as “corporatism”.
I don’t really see anything about the communes, the economy is not socially owned (not run by cooperatives) and the social aspects are veeery limited.
You can do it in a multitude of ways. The French for instance elect their president by voting twice, the first time they vote for their favorite candidate (and the parliament), the second time they vote for either of the two candidates that got the most votes (a run off)
There are other ways, like ranked voting, or you could look up parliamentary republics for an alternative form of government.
Read up on what happens in the rest of the world, at this point, we, as a human species, have tried pretty much everything
Or for anyone really. Anyone in a position of strength that is. That’s the art of the deal, try to bully the weak or bend over otherwise.