If it's a guy who had multiple wifes etc...in that case you'd probably have to pick a favorite wife, and re do the marriage legally in that specific country.
Watchtower did an article about such a situation. You have to remain only with your first wife, and you don’t have to re-marry her since it’s already the only legal marriage, as far as Watchtowers western-centric eyes are concerned. Which is funny, considering how focused they are on the polygamous Old Testament and it’s “principals”.
Indeed It’s not that uncommon, or at least it wasn’t back when watchtower was making converts in the 70s, 80s and 90s.
You’d Probably imagine it would be relevant to converts in Nigeria or Mali, but actually western “polygamists” are told the same thing....ie people who divorced their first partner and remarried before they became JWs. Because I’ve known people who were told they couldn't be baptized UNLESS they asked their first spouse if they wanted them back. Fortunately they never did. But it they had, the poor publisher would have had to leave their current partner and remarry their ex (first) spouse!!