You probably would have to ban entities like corporations, partnerships, and non-profits from endorsing a candidate. It would essentially extend and make permanent the concept of Purdah to those entities. Purdah is the state of affairs during the pre-election period in the UK where entities like local governments and the Civil Service can't say anything that might prejudice the outcome of an election, though I can't argue that it wouldn't be a very draconian policy and doing something completely different to the original intention of the concept.

I don't think having very strict rules about the relationships between corporations/non-profits and politicians is necessarily a bad thing in itself, in fact many would see it as a good thing that further protects democracy from manipulation by private interests. However, I do see the other side of the argument in that it would probably open its own can of worms especially in areas like freedom of speech. The whole idea does start to unravel if your conception of free speech applies to entities like corporations as well as individuals. Unsurprisingly I lean towards the idea that it doesn't, but I can also see some very valid arguments for the opposite as well.

It could well be a moot point however, I'm not sure how well these "not-parties" would do once society had got used to a few elections without parties and experienced the relief that would come from making politics much less adversarial (I suspect arguments between friends and family would be less common without the tribal labels backed by billions of dollars of "enrangement is engagement" for example). We can probably get some idea by looking at extant "not-party" political entities like charities, NGOs, and lobby groups to see how effectively they influence elections today.

> You probably would have to ban entities like corporations, partnerships, and non-profits from endorsing a candidate.

This makes it practically impossible in the US; so long as not coordinated with a formal party or candidate committee, it has been ruled a violation of the First Amendment to even limit expenditures on promotion of a candidate by private entities; to outright ban such actions would be a more flagrant violation.

> I don't think having very strict rules about the relationships between corporations/non-profits and politicians is necessarily a bad thing in itself, in fact many would see it as a good thing that further protects democracy from manipulation by private interests

You cannot “protect democracy from manipulation by private interests”; the concept is incoherent. Democracy is the aggregate of private interests determining the public interest.

> It could well be a moot point however, I'm not sure how well these "not-parties" would do once society had got used to a few elections without parties and experienced the relief that would come from making politics much less adversarial

We’ve had the absence of formal parties, politics was violently adversarial and formal parties emerged from the adversarial factions.

You cannot alter human nature by abolishing formal parties, which are, again, a symptom not the cause of political factionalism.