You know that canonically it shows up in unnamed houses other than Mercere, right?
Not aware of it, don't recall reading it anywhere. Care to point me in that direction?
But otherwise, Houses of Hermes: TL specifically states Mutanteum Magic is in the blood of the line.
Now, the mastery abilities, those are available to magi who study with Mutantes magi.
In HoH:TL. HoH:TL specifically states it is in the blood of that line but not specifically in that House. I'll get you a quote later.
The Virtue description says "most" are Mercere, so that is a point. But I also spot a Heroic Virtue (Gift of Tongues).
A lot of cherry picking.
Try a simpler more straight forward concept.
Mulled it over and came up with an idea...
Father was a necromancer. Mother died during pregmamcy but father zombified her to keep the child alive. Then dad tweaks out or dies, and the other Tremere give her over to you.
for V&F's, I suggest...
+3 Mythic Blood (from mother, power to animate dead)
and etceteras. Don't wanna tinker that much. No Redcap stuff. Nix Legacy and Mutantam magic. Mythic Blood allows for Heroic Virtues and doesn't impact the Vim Lab Total for opening Arts.
I had thought of something like that but Tremere can't have Mythic Blood by the rules (yes, more Tremere Certamen focus issues). Could I get Mythic Blood without the focus for 2 and then use the Tremere focus? Of course, this costs Gentle Gift, too, so it may not work out great anyway. I'll think on it.
Replace the Mythic Blood focus with Potent Magic.
Assuming we can settle on an acceptable mix of virtues for the apprentice, what are the troupe's thoughts on Vocis arranging for a Tremere InVi specialist to open her Arts? I realize this kind of request is well above the resources normally available for a magus of my rank and would expect to be heavily indebted to some prominent Tremere magus for quite a while. We could also say that my parens could do it (presumably with my assistance) if the troupe is feeling particularly magnanimous. 
What are you trying to preserve?
Looks like Animal Ken and Unaging. Both are central to Callen's concept. I need an InVi lab score of 40 to preserve them. Mine is only 30 after accounting for my familiar. I could change a couple third cycle seasons and get to 33, but that's not close enough to make any difference. Getting any higher would require more changes than I'm willing to make.
For a companion, I know Mark prefers Redcaps, but I was wondering whether it might be acceptable to play some kind of administrative chap in service of House Mercere, who didn't make the cut as a Redcap. Any thoughts on the matter?
I'm not so sure he prefers Redcaps as much as he likes them, they fit, and a couple players chose them. I expect he would like other concepts that fit, too.
I spent time thinking on this (outside of many hours doing work - try to keep both hands functional if you want to stay efficient). I like this. I'm not keen on Mythic Blood, though, because not taking Gentle Gift lessens my desire for Gift of Tongues and because I generally think it's a poorly balanced Virtue. I'm debating Gentle Gift with Linguist (which also works for writing - Gift of Tongues does not). I'm toying around with dropping Gentle Gift to Inoffensive to Animals, too. Need to think a little more and make sure the concept doesn't get scattered.
Serf's parma, tired: Isn't there a template in RoP: M for child of the dead or something like this? In the magical humans chapter? I can't recall if it exists, and if it does, if it's magic humans or humans with magical powers, but you may want to take a look.
And the necro father zombifying the mother and all? Wicked 
Yes, there is, which is some of the inspiration I'd mentioned. But do you really want me making an apprentice with Magic Might?
Yes, that is fitting. I didn't want some tragic little girl, rather she is happy with how things turned out. Rather I had this image in my head of a sort of cross between Jane (Twilight) and Alia Atreides (Dune) - a young-looking girl who is mentally much older and is a touch scarey. I'm moving more in the scarey direction which is why I'm moving away from Gentle Gift.
Unaging fits the concept, much as a vapire never ages.
Things that do not seem to fit: Gentle Gift, Animal Ken, and Gift of Tongues.
Animal Ken seems like a waste of a Virtue point and xp, and is the only roadblock for opening the Arts. I really suggest dropping it.
I would think Blatant Gift would best fit here.
Gift of Tongues. Meh. I can let it slide. But it doesn't make sense.
There is also the Orphan Born template from RoP Magic. Start with a low might score (5?) so she can still learn, and chuck things like Unaging and Secons Sight into Qualities (which do not impack the InVi lab total).
Again, Animal Ken is a nonsensical choice for zombie girl. Second Sight makes much more sense.
Unaging fits the concept, much as a vapire never ages.
Things that do not seem to fit: Gentle Gift, Animal Ken, and Gift of Tongues.
Animal Ken seems like a waste of a Virtue point and xp, and is the only roadblock for opening the Arts. I really suggest dropping it.
I would think Blatant Gift would best fit here.
Gift of Tongues. Meh. I can let it slide. But it doesn't make sense.
There is also the Orphan Born template from RoP Magic. Start with a low might score (5?) so she can still learn, and chuck things like Unaging and Secons Sight into Qualities (which do not impack the InVi lab total).
Again, Animal Ken is a nonsensical choice for zombie girl. Second Sight makes much more sense.
Does Might impact the InVi total? I was actually assuming characters with Might couldn't be magi.
Well, remember I'm trying to choose one side or another. Those fit the earlier version of being an expert communicator.
That was why I was looking at shifting the concept.
Do they really not? I could certainly make an Orphan Born with a low Might. I thought they and powers and the like interfered. I'll look at that again. I guess I mixed something up.
Still has the InVi40 issue.
He's saying magical Qualities are not equivalent to supernatural virtues/powers for the purposes of opening the Arts. I don't really understand (or agree with) that interpretation, but if he uses it you can dump all of your supernatural virtues into the Qualities bucket and any magus with 5 in all Arts can open your Arts.