It used to be the case that for the second person singular we would use "thou" and for second person plural we would use "you". These days, the "thou"s have been replaced with "you" except perhaps in the Southern USA.
Now, what if I want to emphasize that I'm addressing the plural rather than the singular? e.g. when talking to a person who's also representing a group? Would it sound super-weird if I said: "Pleased to make you all's acquaintance" instead of "Pleased to make your acquaintance"? Is there another way to say that?
Edit: The register of this phrase would be somewhat informal, almost tongue-in-cheek, within a formal encounter with the representative of the group.