If a mug belongs to my sister’s friend, do I say, “that’s my sister’s friend’s mug”?
That’s my uncle’s dog’s bone?
While technically correct, I think the SDMB’s grammarians would suggest rephrasing to something more euphonious.
Correction: That bone belongs to my uncle’s dog.
[Not sure about the legalistic accuracy of “belong,” in this case. Maybe we can start a thread on that]
How about my son’s boss’s wife’s best friend’s brother’s friend’s uncle’s dog’s bone?
Actually, a double possessive is something of the form friend of mine. The examples given in the OP are just fine as they are noun phrases in sequence.