The usual rule for indicating multiple owners using using apostrophe-s is to omit 's from all except the last owner in the list. So:
Tom, Dick, and Harry's car is the blue one.
But what if I am one of the owners? Polite custom would typically have the speaker place himself last on the list, so would it be:
Tom, Dick, and my car is the blue one.
which follows the rule. Or would this form be preferred?
Tom, Dick's and my car is the blue one.
Aesthetically, I prefer the latter. And it really only bends the rule, rather than breaks it, to become:
"Omit the 's from all except the last owner in the list to which it would otherwise apply."
That would also allow for other, and even multiple pronouns:
Tom, Dick's, your, and my car is the blue one.
But that's just my opinion. Does anyone know if there is an authoritative position?