The first thing you'd have to say is that it all has to be open and aboveboard; if Spouse1 is already married to Spouse2 and Spouse3, they'd have to ALL legally consent and sign papers to that effect before Spouse4 could be added to the marriage. Public notification of some sort, like an add in the local paper, also.
That would be assuming you allowed "add-ons" after the initial marriage.
To answer the question, I would probably stand neutral and neither support nor oppose, depending on the details. If the law enabling polygamy looked badly written, ill-considered or otherwise not covering all the bases that needed to be covered, I might oppose that particular law.
Polygamy has a long established history and was a successful family/reproductive/child-rearing institution for millenia in many cultures. Therefore I have no particular societal objections to it, nor do I have any substantive moral criticism to make, though I consider lifetime monogamy to be more ideal.
On consideration, it is possible that polygamy might actually make marriages more stable and provide some advantages in childrearing. A man with three wives already has his "variety" built into his marriage; perhaps that would cut down on adultery. Joe and Jane might have regular jobs while Mary and Sue tend to the home and the children.
IIRC the OP said "polygamy". Whether he meant polygamy alone, or also polyandry or polyamory I don't know, though I would speculate he probably did mean "group marriages of whatever makeup". Historically polyandry has been practiced but rather rarely; offhand I don't know that polyamory or group marriages have any historical precedent. The idea of polyamorous or group marriage doesn't blow my mind, though, having read a lot of Heinlein growing up. :mrgreen:
However the social and interpersonal dynamics of such arraingements ought to be studied and given careful consideration before we go there. We don't want to frack up the institution of marriage more than it already is, we'd want to have some idea of how well polyandry or polyamory would work before we instituted such plans.
Polyandry would be reproduction-neutral: that is, one wife and multiple husbands would produce no more children than one husband-one wife, because there is only one womb involved.
If all of that were legally instituted, I think polygamy would be somewhat uncommon but the most popular; polyamory/group marriages the next most popular; polyandry the most rare. I doubt there are many men who would see benefits in sharing a wife with one or more other men, and as noted the historical precedent is relatively rare.
At any rate, it is an intresting question as there is much to discuss on the subject. :mrgreen:
Does anyone here have friends who live in a polyamorous/group relationship, regardless of the lack of legal recognition? I'd be curious as to any insights you might have. I knew a fellow who lived in such a household, a neo-pagan group to be specific, (and yes they had kids), but we didn't know each other well enough to discuss the juicy details, lol.