Today in chat we spoke briefly about an earlier discussion I had had with Cerberus in Latin. (In case you did not know, we have a chatroom for this site.) I realized that I do not know how to put both ego and Cerberus in a possessive form together to refer to our discussion. Would colloquium meum et Cerberi be valid? These "mixed possessives" look weird. Of course I could say colloquium inter me et Cerberum, but what I want to know is whether one can combine possessive pronouns with genitives like this.
Eugene McCartney has an article in Classical Philology (XIV 3 July 1919) entitled "Greek and Latin Constructions in Implied Agreement" that mentions these constructions in its opening notes.
While talking about the "closeness of the relationship between the genitive of possession and the possessive adjective," he cites the coordination of the two in the same sentence as supporting evidence. He gives numerous examples that correspond to the OP's example sentence:
Cic. Fam. xii.4.2:
summa laus et tua et Bruti est
Caes. B.G. iii.20:
calamitatem aut propriam suam aut temporum
Verg. Ecl. iii.1:
Dic mihi, Damoeta, cuium pecus? an Meliboei?
Ovid Met. iv.680:
nomen terraeque suumque
Ovid Trist. i.3.97:
nataeque meumque corpus
He also cites some interesting (non-possessive) examples where adjectives are coordinated with the genitive, to further demonstrate that Latin allows this:
haud sane incruentam ancipitisque certaminis victoriam.