The more interesting question is if you can have a functioning democracy with only two parties. If you look at the current US situation I see no reason to be optimistic about it.

The problem looks unsolvable. A root cause is the winner-takes-all voting system which makes it almost impossible for new parties to get elected. And none of the two parties has a real incentive to change the voting system.

If you change to ranked-choice-voting then you don't have to form 2 factions to capture votes.

Democracy can certainly exist without political parties, but in any open democracy political parties will naturally form in any sufficiently large system simply because it's the optimal strategy for politics. Pooling resources and a shared platform provides advantages at both securing votes and legislative working after election.

Wasn't the informal natural of 19th and early 20th century Italy politics one of the factors that gave rise to Mussolini?

I mean this is more vague memories from school which probably oversimplified factors. I just remember it mentioned that 'political parties' were more informal groupings around outsized personalities leading to clientalism and cronyism.

Sure. You can have one party that does everything. Just ask the Russians.

We cure can't have it with, so let's try.