I came across your and Mr X's publication
I came across you and Mr X's publication
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CMOS 16th edition says in 7.22 that it depends on whether you mean the nouns as a single unit or as discrete units; that is, whether the object possessed is the same or different for those two nouns. Since you're talking about two authors responsible for a single publication, not two authors of multiple publications, the nouns are a single unit. "I came across you and Mr. X's publication" is correct.
But there's no question that it is awkward because it's in the second person. (Compare to this third-person sentence: "I came across Dan and Steve's publication.") Reworking the sentence is definitely the way to go.
According to Garner's Modern American Usage by Bryan A. Garner, correct usage would be, "'Thanks, Dad....It was through your's [read your] and Mom's hard work and guidance that I have come this far.' Ginny Rudy, "Traveling in Memory of Dad," Pitt. Post-Gaz., 26 Dec. 2000, at E3." (Here, the read version, which is your, is correct).
Singular unit when both parties are part of a single topic, transaction, etc.
example: 'You and your brothers'
You wouldn't say 'Yours and your brothers' Two many pocessions-there are not multiples of 'You'. Brothers is showing ownership of the 'subject'. You can't both have plural ownerships hence the word 'and'