"Balance of power" diplomacy was first formalized in 17th century Europe. The basic notion is to throw one's support to the weaker side to keep a single actor from dominating the arena.
The key future U.S. Middle East policy is to maintain a balance between warring Sunni and Shia forces there. Continued warfare between the two main branches of Islam is in the geopolitical interests of the U.S.
Our role should be to root for the underdog, whichever side is weaker gets our tacit support.