Although - in principle - I'm all for polygamy, there are highly significant problems.
Tax treatment: How should tax brackets be defined for polygamous marriages? What exclusions for AMT and estate taxes should apply? What income thresholds for various tax rules should apply? What "standard" deduction applies? What are the inheritance rules? What is the federal poverty level for polygamous families. What is the "state of residency" and what rules apply if the marital partners live in 25 different states? And a host of other questions made exceedingly complex when marriages can consist of 2, 3, or 10,000 individuals. Anyone who claims such problems are easily solvable is being either dishonest or in denial.
Obamacare: How would the rules for Obamacare be affected by polygamous marriages?. Again, there are HUGE problems.
Company perquisites: How do companies handle perks when an employee may have 100 spouses and 200 children?
What are the divorce laws for polygamous marriges? What is "community property?" Who gets custody of children?
What about bankruptcy laws? Credit ratings? Joint bank accounts? Who gets to decide when medical treatment should be withheld?
Can a person be a spouse in more than one polygamous marriage? What about immigration laws? What about incest laws?
Plus, think of the AMPLE opportunities for fraud in polygamous marriages.
I could probably come up with many, many more complications caused by polygamy. Complications which are completely absent with two-person marriages. And ALL of these complications would need to have clear-cut solutions before polygamy could be implemented.