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I don't know how you would go about banning parties. You would have to ban almost all forms of cooperation.

I agree with Madison that you can't treat the causes of factionalism, you can only mitigate its effects. Madison argued a large government with many members makes it harder for one faction to seize a majority.

Unfortunately, the founding fathers fucked up bad when they chose first-past-the-post/plurality as the voting system. Social choice theory shows that plurality voting will naturally gravitate towards a two party system. No third party can get a single toe in the door because of the spoiler effect. Plurality's only benefit is its simplicity, everything else about it is somewhere between bad and horrifying.