Yes, definitely, I think that giving polygamy marriage benefits would create problems. It not only would create problems within the family unit but also with money and tax implications. Who would be the "spouse" on tax forms if someone is married to multiple people? It just wouldn't work out and should not happen.
Before gay marriage, the "1 man and 1 woman" argument could be sustained...Because that's the way legal marriage in America has always been. Now, with the Supreme Court ruling that marriage is a matter of the heart, and gender plays no role...There is no longer a supporting argument to deny plural or corporate marriage of convenience.
Let's say 2 couples are compatible and decide to live communally for financial reasons as well as beneficial support (more adults to watch the kids). There is zero reasons that these 4 adults cannot be married and receive all the benefits afforded to spouses and family members. Same with 1 man and multiple women, or 1 woman and multiple men. Anything other than free association is discriminatory based on individual bias.
Polygamy Marriage benefits would cause problems, but the problems can be solved just like most things. There was a time as most know (hopefully) that women had no rights,. When women first gained rights, I am sure that many laws and policies had to be changed, but the people got through it.
If there is a problem, there can be a solution
If you take out the Mormon and Muslim concepts which tends to be the real issue here; and use clear logic; the only real issue is the political crap. All the arguments used against polygamy are the same that were used against same sex marriages, and earlier still, so called Mixed Marriages in regards to ethnicity and religion. Thinks about sexual orientations. If two bisexual women arer involved with one another and the same guy, it's fine. But if they commit to one another its suddenly illegal. That defies any rational thought. Its OK for them to have sex, but not commit in marriage. If said either or both women had children legally the father is responsible for both children through things like child support. Polygamy was only made illegal in the first place as an attack on the Mormons originally even though that violates the freedom of religion in the Bill of Rights. I do not support Mormonism myself for many reasons. However; To "Define Marriage" today is itself a violation of the separation of Church and State. The moment you have to get a marriage license for a Ritual which itself is a religious practice all the same no matter how you try and split hairs; is also a violation of separation of Church and State. Simple really.
Problems are events that usually have solution, and if they do not then they are facts of life. So opening up a marriage into a polygamous union, is a choice that two partners make and as long as those choices are conscious and well considered, then what lies ahead are opportunities for growth and self improvement and as well as deriving more pleasure in life by meeting new people and extending new relationships.