My friend at The Camel's Nose argues that the U.S. should be wary of "buck-passing" in the Middle East, where we take on all the costs of providing public goods like security. I agree with him, but for different reasons.
He says we have no special obligation to countries like Libya and therefore we should conserve our resources by working with others.
For me, whether one has an "obligation" or not isn't so important. Nor is whether everyone lifts their fair share. Rather, it's just a matter of costs and benefits.
Working with others tends to decrease economic, military, and moral costs of intervention, but it does entail some loss of efficiency. At the same time, international cooperation also increases the likelihood of success. In short, costs go down, benefits go up.
But that doesn't mean there's a general rule that intervention requires multilateralism. Some interventions, even with support, just aren't worth it. Other interventions, even without support, are still worth it.
In cases like Libya where there are good arguments for and against intervention, international support - or the lack thereof - can tilt the scales.