The only viable argument against plural or group marriages is that it makes divorce incredibly complicated. (I’m assuming for the moment you mean “marriage” in the legal sense, of an offically recognized status.) But the problem with that is that we already have a very similar situation—the legal partnership. A legal partnership can have many different partners, with different degrees of investment and ownership; and when one of the partners wants to leave, it can be made to happen in a nice structured way. It doesn’t quite handle the situation of children gracefully, but I don’t think pair-marriage divorce does that either, in the general case.
I know a few people who are practicing polyamorists, and I’m very good friends with one. He says that the single biggest adjustment is that you have to stop thinking “Is my partner giving me everything s/he can?” and you start thinking “Am I getting everything I, personally, need?” And the reason for this—well, let’s take a single need. Some people are very tactile and need a lot of snuggling. Others need less, or are very physically standoffish. In a pair relationship, the question you ask yourself is, is my partner having his or her needs fulfilled elsewhere? In a group relationship, the question you ask yourself is, am I getting as much snuggling as I need? Are my partners getting as much snuggling as they need? And if you really are getting as much snuggling as you need, then being jealous because your two partners are being tactile with each other is just silly.
It’s that shift from “am I getting everything I possibly can” to “am I getting everything I need and most of what I want” that makes the real difference between monogamy and polyfidelity.
And I think group marriage is only a resource-consumption problem if all the relationships are structured the same way—all with one man and many women, or all with one woman and many men. In a society where men and women have equitable power and status, you’re likely to wind up with mixed groups of men and women, and the one man with three wives is likely to be balanced out by the one woman with three husbands and the two men and two women in a group.