From a societal point-of-view, polygamy doesn't end well:

• Almost invariably, polygamist societies end up with a few high-status men with many wives. There are cultural and biological reasons behind why this ends up being much more common than the opposite.

Then regulate against that.

• As a result, there's going to be a significant group of under-class men who won't be able to find a spouse simply because there aren't enough women to go around. If the top ten percent of men in a community

I read this argument already (in fact it was copied and pasted multiple times). Easy, put a limit. Also this claim in itself is sexist. Women have jobs too, women don't just inherently try marrying wealthy men.

average three wives, then one-fifth of the men won't be able to get married. So now you have a huge chunk of restless, frustrated, and disgruntled young men who are going to cause problems.

Again, a bit sexist. Especially when u factor in polyandry. Polygamy doesn't always have to be one guy and 5 girls.

• Even if you narrow your scope, there are still problems. Polygamous marriages tend to be more unstable and are characterized by much higher levels of violence and stress. Sister-wives and half-siblings tend to be jealous and competitive. The husband tends to spend his surplus resources on acquiring more wives rather than investing in the wives he already has.

Then allow for divorce out of the marriage, again sexist. If a specific family has a problem with this, great! Divorce. Simple answer.

Take a look at this article from The Economist for a more detailed argument against legalized polygamy.