> The problem is that the US constitution was written before people realized that the natural consequence of that type of constitution is a two party system.
The two party system is a consequence of using first past the post voting, which the US constitution doesn't even require. Use score voting instead, which can be done by ordinary legislation without any constitutional amendment, and you don't have a two party system anymore.
US "parties" are giant coalitions compared to the "parties" in parliamentary democracies. You're solving a problem that doesn't exist.
Change the American voting system tomorrow and legislators will belong to different nominal parties that end up forming precisely the same coalitions.
Love him or hate him, Trump is a great example of this - in 2016, Trump effectively formed a new party focused on anti-immigration and protectionism, which rapidly grew to dominate the "conservative" coalition. But those other parties, ranging from libertarians to the Chamber of Commerce (highly pro immigration and highly pro free trade) parties are still there in the coalition.
Are we reading the same constitution?
Article II, Section 1
> The Person having the greatest Number of Votes shall be the President