Someone wants to be able to use their Shapeshift ability more readily in Dominion auras. Can a magus use some kind of magic to make their effective rank in the ability higher, and thus making the Divine penalty not as onerous? What kind of TeFo combination and base level would be appropriate for this goal of giving them a +3 to their shapeshift roll?
Such a question leads to wondering whether other abilities could be boosted, such as Entrancement or Second Sight.
Why not just class his Shapeshifting as a Divine Supernatural Ability from the get-go? Then there's no aura penalties anywhere and you get bonuses in Divine Auras.
Boosting a power in the way you want would probably wind up being MuVi, the same combo that brings Wizard's Boost (Form) spells. A major change adds a magnitude, a total change can add two, that's roughly equivalent to +1 on a roll per magnitude (maybe?), and the spell has to be powerful enough to boost the end product of the supernatural ability. In terms of Shapeshifting, you're boosting a Pers/Sun/Ind MuCo(An) spell.
Hermetic Magic is bad at this sort of thing. Natural Magicians can manage much better results, IIRC, directly adding to totals and the like.
Hermetic mages are quite good at this sort of thing. They just have to do it ahead of time. Magic Items, in canon, are not affected by Auras, once built. Make a cloak of Shapeshifting in your lab, and problem solved. Now, if you wanted to keep using your "Supernatural Ability" (Because you like the fun of botching?), an Item of Quality (Animal Hide is +7 to turn into Appropriate animal, that should be all the bonus you'll ever need....) will do the trick!
Ahem. Not the same thing. 
Now you're talking, though you'd need one item for every form you wanted. And you'll need a Verditus with Philosophae of 7 for that much bonus, so I think you're more likely to get +3-4, which would be enough to deal with low end Divine auras. You don't need to Shapeshift inside a church, right?
Really, though, Hermetic guidelines need to be updated to do stuff like grant Virtues/Flaws and grant bonuses to Abilities. It's part of too many non-Hermetic magics that would likely have been integrated early in the Order's history, really. It seems like it was omitted as a deliberate design choice in early 5th and every author since has been cramming it into non-Hermetic magics just because the Hermetics can't do it.
Well, it's suggested by Magi of Hermes' Marcus of Criamon that you can give a +3 to a physical ability/characteristic from the MuCo base 2 guideline, and in some very specific cases even a higher bonus. So, the more general the bonus may be applied the lower the bonus overall. This is also inline with granting some of the bonuses available from virtues...
Leaving aside your mocking of the House of Masters, I would point out that any normal Verditius is probably going to start with a Philosophiae of 4 or 5. It is, after all, one of two skills used all the time by that House (along with Craft). Verditius Runes are sweet, and the kicker you get from Elder Runes is something it would take a very "special" Magi to ignore. With specialization, I think an assumption of five to seven is more correct.
It is relatively challenging to create a magus character just out of gauntlet of Magic Theory 4 or 5 AND Philosophiae of 4 or 5. Both at 4 is 100 xp, which is a huge chunk of XP. And both abilities are required to get the bonuses. So, no, such a character would not be normal, and would require a lot of virtue points to get both abilities to such a high level immediately out of gauntlet, and even then they would come at the expense of other things, like Arts.
An average Verditius will likely not specialize in Items of Quality. Anyone doing it for a business likely will have at least a 7 Philosophae, probably more. It just means that you'll need to go to the Verditius for a reputation of crafting IOQ's instead of the guy who has a rep of forging magic rings.
This may actually be putting the cart before the horse. I think any Verditius who has a strong inclination (puissant/affinity/etc) in Philosophae will be initiated into Items of Quality post-haste, for the good of the House.
Puissant/Affinity probably need to be doubled to apply to Magic Theory, too. Otherwise one ability is still limited by the other's progress. Philosophiae is important for all Verditius, not just those who would pursue Items of Quality.
Philo score of 4 or 5 is probably good enough for a lot of Verrditius, as it will get the vast majority of bonuses.
Well as far as Virtues Go, I don't read allowing non-Hermetics to provide them as a "they can do it because we can't" situation. I suspect it has more to do with imparting a broad range of effects with out needing a lot of space. For that matter I'm not certain hermetic magics seeming inability to impart Virtues is a deliberate design choice. Hermetic Magic is very well described and is very concrete it it's effects, while most virtues are fairly abstract in their nature. It's not exactly accurate to say hermetic magic can't impart virtues. Certainly it can grant the equivalent of the more obvious and concrete Virtues like Large or Tough. It's just hard to figure out what hermetic magic can do to make a character better at reading books.
The same goes for Abilities. Aura of Ennobled Presence provides bonuses to a variety of ability rolls. So clearly there is no rule against magic providing ability bonuses in certain situations.
As to "Philo score of 4 or 5 is probably good enough for a lot of Verrditius, as it will get the vast majority of bonuses.", I would think Hubris would lead most of them to raise that score, as well as Magic Theory. Magic Theory times Philo (Once you have Elder Runes) is a LOT of spaces in one's magic items....... (And sure trumps the heck out of Item Attunment, unless I am reading it wrong.).
There is so much else to learn, though. Hubris is just as valid an excuse for raising Arts or other abilities, or making items.
For small bonus, ligatures can be a solution for those who cannot access magi for items of virtue. Agreed, most of the time, it will be a +1, with some luck, a +2. But it is quite likely that if the person is educated (ie, has a score in Philosophae, Artes Liberales or Medicine), it can at least enhance her ability for a given time.
I don't know if it would be possible to find a Formulae assisting a supernatural ability. It has already been pointed that it should fall within the Realm of MuVi, but the final level might be well above the capability of an educated, but mundane scholar.
Not convinced. Verditus Magi are extremely starved for XP. Thematically, they would have their Craft as their highest skill* , and from there I still think that Magic Theory is more valuable than Philosophae, as it's still the limiter on Shape and Material bonuses in most cases. So Craft adds to all enchanting, Magic Theory adds to all enchanting, but Philosophae only adds to S&M bonuses (and its Inner Mystery gains don't eclipse the value of Magic Theory or even Craft).
And then you have to find time to raise Arts and learn spells, not forgetting that Verditus magi get only exposure XP many seasons while making magic items. Once Philosophae hits around 4, its overall value vs the amount of XP needed to raise it make it an unattractive choice.
*I'm of the opinion that a Verditus should be as skilled with his Craft as a mundane craftsman of roughly the same age, especially once Hubris starts kicking in. They can't quite compete because Intelligence is more valuable than Dexterity and they're likely to have different priorities for virtues, but a Verditus being outclassed by mundane journeymen is something most wouldn't stand for.
Well, first, Mr. Prins, I was including the specialty "Natural Philosophy", which at least in my experience, correspondences with Lab work. So read that as 3 or 4 if it makes you feel better. Second, Why not Affinity and Puisant for both? It's just one point more then Mythic Blood or Major Magical Focus, while being far more useful. And as a happy perk, neither are Hermetic virtues. Heck, next time I get to play, I will get both in Magic Theory, Philosophy, and Craft. Still four points for virtues, none of which will be Hermetic. I will learn the Hermetic virtues in gameplay. (As to maximizing Craft, gosh, that was the first thing I did with Items of Quality.......)
You can only have Puissant or Affinity in two skills each... That's one Craft and Philosophiae, or one Craft and Magic Theory, or Magic Theory and Philosophiae, or two Crafts (do not recommend)... But yeah, you gotta pick two (or, I suppose, one and two halves, perhaps Puissant+Affinity on Craft, Puissant Philosophiae, and Affinity Magic Theory).
Where do you get that you can only take each one twice?
Silveroak is right, the restriction on Puissant (Art) is 2, there is no restriction on Puissant (Ability).
Aw, snap. I'm an idiot.
... Incidentally, I have two months of bad SGing to apologize to some people for.
I agree that the "average" freshly guantleted Verditius will have a lower Phil score, but when you buy IOQ's, you are going to the IOQ specialist, not the fresh-faced kid just out of college. Because Phil is not a hermetic ability, high quality summa and tracti are going to be plentiful and cost pocket change, especially if you read or can translate Arabic dialects.
My point is that even a few years out from guantlet, the Phil score is going to rise quickly, especially compared to things you have already invested heavily in (such as craft and MT). Studying Phil is going to have a very high value to cost ratio your first 5-10 years.