Inherited traits question

I just had a strange thought; can a family member get multiple 'family' traits? That is, can a Baktrian 'Heterogenes' who is adopted into the 'Gens Scipii' get both traits or any other permutation thereof?
Might sound silly, but I remember from vanilla RTW and RTR that when you adopt a foreigner into your family, any children said foreigner sires has both a new-faction-specific picture, and name.

Most likely, traits you get for that character will be a bit odd due to the double ethnicity.
The children will probably just be SCIPII, but they may even have a randomly different ethnicity assigned.
Traits and character pictures aren't connected. Any character that starts in a faction can only have a picture from that faction, no matter their father.