Another one is Afghanistan. America had to backtrack on their initial Afghanistan policy of going it alone and went back to the UN. Prior to UN decision or sometime in 2004 (no longer sure of the year), US was lobbying massively with NATO member nations to agree for them to back up their UN proposal that NATO be deployed in Afghanistan. They couldn't take on Afghanistan all on their own as they did not foresee the difficulties they would be encountering in Iraq.

In the end NATO was deployed to Afghanistan backed by a UN mandate to do so.

Would be terribly unjudicious for the US to act unilaterally. Roughly put, just won't work anymore or not unless they use their nukes.