Given polygamous marriages have existed for thousands of years, and remain legally recognised in over 50 countries today – mostly Muslim majority states, although some countries without a Muslim majority legally recognise it for their Muslim minority only, e.g. India and Singapore, and some African countries, e.g. South Africa, allow it for people of any religion (although South Africa limits it only to members of indigenous ethnic groups which have a cultural tradition of polygamy) – I don't see what's so hard about legalising polygamy in Western countries. This is not some radical new idea, it is something very common in human history, and even legally allowed in roughly a quarter of the countries in the world today.
Western countries would want to make the institution non-discriminatory, which would mean: (1) allow women to have multiple husbands, as well as allowing men to have multiple wives; (2) allow same-sex polygamy, so a woman could have multiple wives or a man multiple husbands; (3) require knowledge and consent, so a person cannot marry a new spouse without consent of their existing spouse(s), and the new spouse must be aware of those existing spouse(s); (4) open to people of all religions and none, instead of being for Muslims only, or being for members of certain ethnic groups only
(3) actually already exists in some countries – for example, Singapore requires consent of existing spouse to contract a valid polygamous marriage – so that element isn't new. (Although some other countries allow a husband to take a second wife without the first wife's consent.)
(4) isn't historically novel either – although in recent times, Islam has been the only major religion to commonly allow polygamy, it has been widespread in human history and has never been unique to Islam. Indeed, polygamy for non-Muslims is legal in a number of African countries, for example South Africa – former South African President Jacob Zuma legally has four wives, and he isn't Muslim, he follows Pentecostal Christianity
Nor is (1) historically novel – a number of traditional cultures have polyandry, although in the contemporary world no country legally recognises it. (Well, apparently, polyandry is theoretically legal in Gabon, but unknown in practice.)
The only element of the above that's truly historically novel is (2), allowing same-sex polygamy. But, I don't see how that historical novelty is an issue. There's nothing special about same-sex polygamy which makes it somehow more complex than opposite-sex polygamy is.
> For example, would merely removing the prohibition on bigamy be sufficient? Or do we need group marriages rather than some combination of pairwise marriages between members of the group?
Compared to multiple concurrent two-person marriages, group marriage is historically very rare, and isn't legally recognised in any country today. Given that, I think it would be most logical to start with pairwise marriage only. If people really want group marriage, they can campaign for that separately. Given a group marriage can be simulated by a collection of pairwise marriages between the group members, does the lack of group marriage – in a society which allows polygamous pairwise marriage – really pose any issue?
> Once gay rights advocates agreed on gay marriage as a goal, it was almost immediately clear how gay marriage would work. This simply isn't the case for poly marriage.
That really isn't true. Given over 50 countries worldwide already have poly marriage, we can just do what they do, minus the discriminatory parts, none of which are essential to the concept.