Polygamy can benefit society.

In polyamory, maybe Mary and Sally are still married. In polygamy or polyandry, no.

This is definitely a situation where the law books would fatten.
Although I hate to say it, this sort of scenario is when civil unions would be useful. Colorado's civil union law (which was for anyone unable to marry but not already married) included survivorship and similar concerns.

A set list of potential partnerships, triad, quad and then exponentially, could have laws set to govern creation and dissolution of the relationship, fiscal and medical and other legal concerns, parenting considerations.