How do I change, for example, "the party/wedding/relationship/... of John and I" into the possessive case (possessive using 's)?

My train of thought goes a little something like this:

The party/wedding/relationship/... of John and I

(John and I)'s party/wedding/relationship/...

(John)'s and (I)'s party/wedding/relationship/...

John's and my party/wedding/relationship/...

Is this correct? I feel like it's similar to the distributive property in math. When using the possessive to denote a shared possession between two or more people, do you use the possessive case ('s) after the name and a possessive adjective in place of the subject pronoun? Any and all help is greatly appreciated! Thanks a lot in advance!