If this ever goes before the SCOTUS, it will be interesting to see how they rule.
Of course, there has been precedent in US law against polygamy. Back in 1878, in US v. Reynolds, the court ruled unanimously against Mormons and their plural marriages. From Wikipedia:
The principle that a person could only be married singly, not plurally, existed since the times of King James I of England in English law, upon which United States law was based.
Of course, this is also true of marriage between one man and one woman. But the court threw that out as well. So they have no foundation any longer to rule against plural marriage.
Man in threesome marriage: ‘This should be the future of relationships’
AUSTIN, Texas, May 22, 2017 ( LifeSiteNews) – Two bisexual women and one man proclaim threesome marriage “should be the future of relationships” and that their threesome parenting is “setting a good example.” Adam Lyons, 36, lives openly with two women, 28-year-old Brooke Shedd – with whom he has a two-year-old son, and 27-year-old Jane Shalakhova – who is eight months’ pregnant with his third son.
SCOTUS would rule whether the law was constitutional or not. Same sex marriage bans were obviously as unconstitutional as inter-racial marriage bans. This article does not address anything at all about what constitutional rights are being violated or what specific path would be taken to even get this in front of the Supreme Court. Much ado about nothing.