I think this is a safe bet. The Institute goes up in a mushroom cloud in 3 out of 4 endings. The other groups needn't have gone down too to have left the Commonwealth. So that leaves the Minutemen, the inevitable rise of an east coast government, and the BoS as some paramilitary country spanning organization intended to keep humanity from wrecking itself again. Then the People's Commonwealth Alliance (name pulled from where the sun don't shine) and New California Republic meet at some point during their expansion, tensions rise and negotions break down, and then we get another case of "War... war never changes." Somewhere in there, the BoS is actually trying to play referee and damage control.