Despite the fact that James Madison thought the system of government they were creating would put partisanship in check, in the practice it created a bipartisan system where parties seem to be above everything.
It kind of worked when America was somehow homogeneous and States were relatively isolated and State politics were important, but nowadays with what happened in Arizona and the reaction from Republicans and Democrats blaming the poor performance on lack or excess of progressivism.
Its clear that America needs a third party, but for a third party to be viable America needs to move towards parliamentary system or find a way for political minorities to be represented.
So instead of having 2 parties that range from extreme left to center and one that ranges from extreme right to center, you would have 3 parties.
One with the left like the types of Bernie Sanders and AOC
One with the center like the Clintons or the Bushes.
One with the right like Mitch McConnell.
And in order to have a functioning government there would be a need to compromise the dominant party would have to ally themselves with another party in order to have a functioning government and thus would work as checks.