There is no visa for polygamous or polyamorous relationships. The UK will not use polyamory against you (or polygamy I suppose), but they simply won't recognize it either for the purposes of granting visas. I am not aware that the UK government has ever bothered to dig into the explicit relationship of two people deeply enough to determine that there was a third person involved with the obvious exception, ofcourse, of multiple marriages to verify legal divorces and current legal marriage status. If he can establish a relationship akin to marriage with a partner in the UK, then he can qualify for that visa. My best advice on this, don't lie. Don't ever try to deceive the Home Office. If marriage is in the cards, one married couple and one married couple only. If that marriage happens to be open enough to involve a third person, that's the business of that couple, not the UK (from their perspective, not mine).