You can't just make a law that insists you have several parties in your system. That's implanting democracy from above, which just doesn't work.
Abolishing the electoral college, replacing majority vote with representative vote and no longer elect governors directly. It's simply unfair that the state where you reside in decides how much your vote is worth, considering someone (in theory) has as much to do with the president as the next guy. The electoral college is made even more undemocratic trough 'First Past the Post', where your vote is ignored if you are a minority. Every vote should be worth exactly the same, and whoever gets the most votes, wins.
As for the election of the senate and the house of representatives, third parties are kept out (and therefor, political minorities also) by having an independent election for every seat, meaning that hypothetically, a state that has 10 seats and where there are 10% vote for party A, 20% for party B, 10% for party C and 60% for Party D, party D would get all the seats. This is while 40% of the voters do not want to be represented by party D. This leads to bandwagoning, where voters no longer vote for the party of their preferred choice, but the party they hate the least which still has a change of getting in. How can anyone defend this system? Representative voting is the way.
This would of course lead to an explosion of parties that are voted into the senate and House, but hey, that's democracy. No longer would there be a single party in charge; Parties would actually have to form coalitions and agree to cooperation, which means that on a variety of issues, middle grounds will be reached, instead of one party getting everything they want.
I am aware of the fact that American politics circle more around persona then around parties, but I'm confident that with changes, that mindset can change. Political participation will rise, because now people can truly get THEIR say into state and national politics. While one can argue that this would not benefit how well the system works, the situation can't really get any worst in the USA. Democracy is, eventually, about the people having a say in how they are governed.