my first idea was between gramny its allie the us and its allies and the soviets and there allies what ramifcations would have and bonus points if you could involve japan or the phillpines or even if i dare say mexico?!
Agree with Hobelhouse, for sure after the Sino-Soviet split the Cold War had a three power aspect with the US hoping to get China over to their side. I wonder if after 1960 you could make the argument for Europe being another player no longer following US policy without question.
For something more out of the box, Imperial Japan one that stays out of World War II. It is able to build up power in the Pacific and thus be a player in Cold War politics, playing the US and USSR against each other.