I feel like this is a topic that, given @sb 's logic, can be debated one way or the other. In his defense, looking at WW1 and the idea of 'entangling alliances' giving way to all out war, you can argue that having larger military alliances increases the chance of war (while also minimizing through deterrence).

There is a... sweet spot, between deterrence being effective, and literally taking so many members that war becomes likely/inevitable whether through accident or otherwise.