> 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.

Are we reading the same constitution?

Article II, Section 1

> The Person having the greatest Number of Votes shall be the President