Oh I have a good one: abandon the two thirds majority needed to ratify treaties.
It would weaken the US in treaty negotiations. Furthermore, it would make treaty ratification easier than passage of regular laws. Treaties then could be passed by a simple majority vote of the Senate - ok, 60 votes, since they would still be subject to filibuster, but so are the laws - whereas regular laws would still need the House. Consequently, you would get presidents, especially if they have the Senate, but not the House majority, go around concluding meaningless treaties with Marshall Islands and Palau, enshrining all sorts of provisions as US international obligations.