When a compound possessive is formed with "and," I think the rule is that both terms become possessive when there are multiple separate objects that are owned, as in "John's and Dave's cars" (John's car and Dave's car). Only the last term becomes possessive when you're talking about a shared object, as in "John and Dave's house" (one house where John and Dave both live).
Is there a similar rule with "or"? Like is there a difference between saying "That house on the left is either John or Dave's house" versus saying "That house on the left is either John's or Dave's house"?