The plurality system inevitably leads to a two-party duopoly; that's called Duverger's law. Just as a commercial monopoly leads to higher prices and poorer service, this duopoly brings more corruption and less responsiveness.
There are several election systems which could improve this, with varying advantages. Instant runoff voting (IRV) is the best-known, but even better systems include Proportional Representation, Approval Voting, SODA voting, Majority Judgment, Condorcet Voting, and Range Voting. Even simple second-round runoffs would represent a real improvement.
Rather than writing an amendment to require just one of these systems - and perhaps missing out on an even-better system that is invented tomorrow - a constitutional amendment should lay out the principles by which election systems should be chosen. These include effectiveness (if all voters vote honestly, gives a result that is well-liked by the electorate overall); resilience (if all voters try to vote so as to gain a strategic advantage, the system still gives good results); and fairness (reduce the chances that a united minority of strategic voters can take advantage of the system to elect whomever they want). All of these attributes can be quantified mathematically and/or empirically, and all of the above-mentioned systems do better - often dramatically better - than plurality voting on at least two of the three measures.