Per title. E.g. right now the US has a mutual defense treaty with the Philippines and also with South Korea. If the Philippines and Korea go to war with each other, who is the US obligated to help?
I imagine this must have happened in history (making this perhaps better asked on the History SE), but I can't find any examples, and in that case this is likely the better place to ask. The closest example I found was US involvement in the Falklands war, but that never led anywhere because the US wasn't legally bound to assist either side:
At first glance, it appeared that the US had military treaty obligations to both parties in the war, bound to the UK as a member of the North Atlantic Treaty Organization (NATO) and to Argentina by the Inter-American Treaty of Reciprocal Assistance (the "Rio Pact"). However, the North Atlantic Treaty only obliges the signatories to give support if the attack occurs in Europe or North America north of the Tropic of Cancer, and the Rio Pact only obliges the US to intervene if one of the adherents to the treaty is attacked—the UK never attacked Argentina.



