If not, why not?
I'll bite.
In principle, I don't see a problem with multiple marriage - I'm presuming you're not using polygamy in the exclusive sense of one person being married to multiple others of the opposite sex/gender, but rather the broader 'group marriage' concept?
In practical terms I can see that there are opportunities for it to be abused, moreso in some cultures than others, and certainly in the more modern settings the history has been typically one man exerting influence and authority and having multiple wives. That history also dates, though, from a period when in most instances marriage for women was one of the few ways for them to secure any kind of future.
Is our culture ready to accept that sort of relationship yet? I don't know, I've known (or, more often, known of) people who've tried to make a go of being part of a three-way relationship: some of them have worked out, others haven't, but I don't know that it's a large enough sample-set to compare to more conventional relationship performance.
O.