I think it's a regional variation. I've said eg Jim and I's . .
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AnonymousIf you are referring to two separate dates, it would be "Jim's and my anniversary." Did I get that right?So, by extension, would "Jim's and my wedding" be understood as referring to two separate ceremonies? I just think your interpretation, although possible, is a bit of a stretch in this case.
Anonymous"Jim and I's anniversary." I don't see any way this could possibly be correct.It’s nonstandard.
AnonymousI was always under the impression that you should avoid plural possessives, but if you must, it would be "Jim and my anniversary" if you are referring to the same day. If you are referring to two separate dates, it would be