To me this is an easier argument than the same-sex marriage.
Like Ron said, there's pretty significant and wide ranging precedent for group families and multiple spouses (certainly multiple wives) being normal and endorsed by society. If the government is going to be in the business of encouraging stable relationships, I'm not sure there's any real argument not to encourage 3 and 4 person families in addition to 2 person families.
My one concern, and it's not insignificant, is that we would want to look closely at ways to ensure that young people, specifically young women, are not being pushed into these relationships by men in positions of leadership and/or religious power over them. It would be very easy to cross into abusive "consensual" relationships, which also has significant and wide ranging historical precedent.
I think this is being brought up when discussing Rep Hill's situation because they are deflecting from the main issue. The issue isn't that she banged a bunch of people, that's between her and her husband. The issue is she entered a sexual relationship with not one, but two of her employees. It's almost universally acknowledged that you can't really get consent in that kind of situation, because as their boss, the idea of quid pro quo is always there, like the elephant in the room. Which is why the federal government (and I'm SURE specifically the House) has fraternization policies prohibiting that kind of relationship.
Were this a male rep with some female employees we'd have already seen editorials talking about how it was probably rape, because those employees couldn't consent in that situation.