I have a sentence that reads: I want to thank you for the opportunity of allowing us to host Michelle and John's engagement party. Is there an apostrophy s after Michelle as well? Should the sentence read: Michelle's and John's engagement party?

Thanks so much
The correct way is: Michelle and John's engagement party.
We DON'T put the apostrophe after Michelle.
I suppose they are giving the party. If it is their party the apostrophe is ok.
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So if I understand correctly, if Michelle and John are giving the party then the correct use would be Michelle's and John's. If a third party (parent) is giving the party (and getting the thank you) then Michelle and John would be considered a singular unit and the sentence would correctly read: Michelle and John's. Do I understand your response?

Thanks again.
Michelle and John's party- they are engaged. Supposedly they are getting married and they are giving a party. It's their engagement party. Using the article after the second noun means that it refers to the first, too. They are conveived as a unit. The apostrophe indirectly applies to the first noun as well.
 Woodward's reply was promoted to an answer.
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