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The title really says it all. When there are two subjects in the possessive, what do we do?
If "Sally's and Mike's bikes" is correct, isn't this ambiguous? (As the phrase could either be referring to the bikes that are owned by both Sally and Mike, or to one bike that is owned by Sally and one that is owned by Mike.) Furthermore, doesn't the sentence "My mother's and father's marriage seems awkward, clunky, and badly thought out" seem awkward, clunky, and badly thought out?
If "Sally and Mike's bikes" is correct, isn't this also ambiguous? (As the phrase could refer to either the bikes that are owned by both Sally, and Mike, or to Sally and the bike that is owned by Mike.) And the sentence "Joe Biden and the President's daughters get along famously," as much as some slash political fanfiction authors may protest, seems far more likely to be saying that Joe gets along with Sasha and Malia than that Joe and Barack have secretly eloped and have had multiple children, who get along with each other well. But if this sentence is incorrect, how would you refer to these clandestine daughters? ("Joe Biden's and the President's daughters" seems to refer to two different sets of daughters.)
Finally, does this get even more complicated when you add pronouns into the mix? ("My and her house" is a repulsive sentence. How can we rephrase it without losing information? (Which "Our house" would certainly do.)