Legislating against polygamy would imply that either every single instance of polygamy is morally wrong (although it is quite possible for healthy polygamous relationships to exist), *or* that polygamy is somehow so attractive that allowing it would open the floodgates to a widespread cultural shift (which is preposterous), *or* that polygamy can potentially hurt other people (which it doesn't).
The best approach here is to fully allow polygamy, but reinforce monogamy through a kind of positive propaganda. Basically, rather than attacking polygamy, it's better to attack the cultural memes promoting it, replacing them widespread visibility of healthy monogamous couples. Make sure that monogamy is what most people will want, and accept (do *not* persecute) the minority that doesn't want it. As long as you manage to create a stable "baseline" for behavior in society and break cultural isolation, there is nothing to worry about.
Basically, legislation is ineffective at stopping people from wanting what they want. The catastrophic failure of prohibition and of the current wars on drugs and piracy are good evidence of this fact. The best weapon against harmful trends in society is propaganda, not legislation: you need to align the will of the average person with something that works well for society. Once that's done, you know that a minority will indulge in potentially harmful behavior, but it's just a minority, so you leave them alone. And if you fail, well, it's pretty clear that only a police state could have any success in legislating against the majority, so maybe you should re-evaluate your position.
Polygamy can only become a problem if you let it spin out of control. The only way that can happen is through cultural isolation: a polygamous subset of society perpetuating the behavior among its own members. They start with the same "baseline" as the others, then add a slight deviation, which becomes the new baseline, and so forth, compounding deviation upon deviation until the group is stuck in a self-destructive loop. Hermetic cultures cause all sorts of problems, though, and I'd rather use a silver bullet to break them than add a whole pile of legislation that's bound to conflict with legitimate situations. Basically, create huge incentives for people to question (or leave) these cultures and make sure they are aware of them. Maximize the exposure of all citizens to alternative viewpoints, facts and rational arguments. I think this ought to do the trick, though I bet many cultures would be scandalized by what essentially boils down to eliminating them through attrition.
