It is not at all clear why Washington should have any interest in assembling such an alliance, nor why any other state should be interested in joining it.
One classical reason for any alliance is capability. A large threat, like that represented by the old Soviet Union during the Cold War or Napoleonic France, may need a critical mass of states in coalition to counter it. This cannot be said of the terrorist threat.
It seems very unlikely that additional warlike and economic resources above and beyond those already possessed by the US could make any difference, or sufﬁcient difference, to compensate Washington for having to share its counterterrorist planning with other states.