Okay, I've seen this touched upon, but nobody has answered it..(that I'm aware of )
What happens if you pass your apprentice around to Magi from different houses? Does this change the basic abilities of the Apprentice? Are the apprentices abilities set when opened? Could this result in a Magus that was more "Cosmopolitan"?
[If I follow the history correctly, (for example) Bonisagus was taught spontaneous magic by Diedne... This seems to indicate that a 'Finished' Magus can learn new 'tricks']
(By "abilities" you're meaning Talents, Skills, and Knowledges, right?)
Since this is not addressed in the rules, just use common sense- it's not like a game of tag where the last master to touch the apprentice wins.
If a Bonisagus Parens claimed an apprentice from a different house, an apprentice who was well into their apprenticeship, the echoes of that previous (and "improper"?) style of teaching would be hard to reverse. So the personal "world view" of that apprentice may well include elements from both traditions, for better or worse, depending who you ask.
As far as Abilities changing... how? Education is an ongoing process of addition- you don't need to forget what you learned in grade school to learn something else in college, and you couldn't forget if you had to.
As far as what a growing apprentice "believes", when two teachings conflict? That's up to the storytelling.
As far as V&F's changing or being added- there's another thread where that topic is being discussed- again, up to the GM/troupe.
They can learn new tricks, just not do them as well as the true masters.
Short version: passing him around is a good way to build in virtues and flaws
IMO if you were to pass yer apprentice around it would depend how much time you spent with him vs others.
Say you give him to the resident Diedne for 15 season in 15 years then they may have the option of taking the Diedne virtue (if the Diedne agrees to actually teach that kernel of knowledge), If you only passed him off fer a few seasons then it may be more appropriate to take FLEXIBLE FORMULAIC MAGIC, or LIFE-LINKED SPONTANEOUS MAGIC.
Same with handing him to a Bonisagus may allow INVENTIVE GENIUS