There is nothing explicitly preventing more than two parties from existing in the US (they do).

The problem is that people tend to become tribal because of collectivist philosophy (most don't even know they're afflicted with the disease, which makes it even more lethal).

Having more parties isn't really going to fix anything if people are still tribalists.

In fact, parties wouldn't matter all that much in a rational society. Many of the US Founders were actually against the concept of parties because they feared what the collectivism and tribalism would lead to (they were right).

Having more of the cancer doesn't seem like a good solution to me. You'll still be ruled by gang warfare. There will just be more smaller gangs. So maybe tyrannical rule by 31% instead of 51%. That isn't much of an improvement.