Not constitutionally, but by using single member districts and our current voting algorithm, the equilibrium is two parties. So we are a de facto two party state.
Why? Two party system is a feature, not a bug.
There's something more going on in the US.
Go check the Dutch or Belgian systems. They have proportional representation and our (NL) current government is a coalition of 4 parties. (Yes, it moves slower, but also results in a more nuanced government and more gradual change)
But the UK is the classic two party system that Washington warned against.