Well, if you're referring to the various Holy/Unholy/Faerie traditions described in the RoP books (as it sounds like to me), I believe it works like this:
A character with the option to learn powers associated with the realm in question, can at any time, join a single tradition and learn that tradition's Favoured Abilities with the usual benefits. I'm pretty sure it's strictly a binary thing, however, and while there's no specific initiation or virtues required, membership is also (metaphysically) irrevocable and permanent...
Characters who qualify for learning a realm's Supernatural Abilities can learn any of them as long as their Study Total gets them a score of 1 in one season. They have to subtract the scores of all the other Supernatural Abilities for that realm, though. If they join a tradition, which is like opening the Arts for Hermetics, they get four Favored Abilities that they can study without having to subtract any of their non-favored Supernatural Ability scores, and from which they don't have to subtract their scores when studying other non-favored Supernatural Abilities.
From ArM5 p166, I thought that you had to have a Teacher teach you, and it was all dependent upon the Teacher's teaching Source Quality.
Which always puzzles me. I would have thought surely the quality of the student should have something to do with being taught a supernatural ability.
As it is, you could equally teach a new supernatural ability to a low-intelligence Simple-Minded, Poor Attention Span student as easily and as well as teaching to a brilliant-intelligence Apt Student with, say, a minor magical focus in Self-Transformation.
Is there nothing a student can have that makes them better at learning new magical abilities/virtues?
The biggest help to an Hermetic maga is, to have the Minor Hermetic Virtue Subtle Opening (HMRE p.51 upper box). But this requires, that her parens had already access to the HMRE p.50 Breakthrough Subtle Opening in your saga.
It's really no different than for being taught mundane abilities. There are Virtues that help you learn more quickly (Affinity, Apt Student etc.); but having raw talent in the ability being taught (e.g. high Dexterity for Craft:Weaving, or having Puissant Craft:Weaving) does not impact your ability score - instead it directly impacts your totals later, when you use the ability. I'm not sure why you'd find this puzzling.
See the Ars Notoria in RoP:D and The Witch-Hammers (RoP:I p131-132) for cases where books are used to teach, so avoiding the bit on ArM p166 where it says "The initial teaching in a supernatural ability must be by Training or Teaching"
It should be noted that both books are not "ordinary books", they are essentially plot devices.
The Divine one explicitly so; the Infernal one being a text that spontaneously changes over time!
They should not be used to conclude that one may, in general, learn supernatural abilities from books.
I must have misread TMRE. I was under the impression that Apt Student didn't apply.
I don't think my SG is running such a saga, nothing was mentioned about extra breakthroughs in play. I am wondering how unbalancing that might be.
My SG did tweak my character's Infamous Master flaw, so that my character's parens was Envious of magi who seemed to have better abilities than House Tremere, and is considered a lying, cheating, thieving bully who stole Hermetic secrets from various Houses and lineages, and used blackmail and legal loopholes to avoid Tribunal punishment. It means in saga that my Flawless Magic character knows every possible Spell Mastery ability, and other House "secrets" such as Jerbiton synasthesia magic,. My SG was getting rather excited about the story possibilities of my character's parens who had managed to learn nearly every Hermetic Virtue that didn't explicitly need a Mystery Cult to open.
I had been wondering, should my character emulate his parens, how he would do so.
Apt Student is useful to learn the (TMRE p.11 upper box) Revised Ability: (Mystery Cult) Lore and helps with (ArM5 p.166) Learning Supernatural Abilities. It doesn't help directly with The Mechanics of Initiation (TMRE p.13ff), unless called for in a specific script.
Unbalancing is not really adequate to described the impact. By conception, Ars Magica is not balanced, but is coherent (you can find plenty of examples in this forum of broken things that can be done with an optimised character fresh out of apprenticeship or with just a few years experiences if you pick up the right virtues amongst the whole range of books).
Having this virtue will just change the paradigm: more mages, with a broader range of skills, borrowed from all kind of traditions. Maybe the apprenticeship duration has been increased by a few years to be able to add more Surnatural skills in each apprentice background
Depending since how long this breakthrough has been made, it can go from:
"negociating" with every edge wizards to pluck their secret (if Subtle Opening was recently discovered), in a kind of race to more power;
to every house has many different "sub-house", where these new, modern traditions have integrated the most useful virtues to fulfill their agenda - possibly House Ex Miscellanea enjoy a raise in power since she has access to the wider range of edgies; if you consider that completion of a mage apprenticeship is like having a bachelor in magic, maybe there are now "advanced" class to get your PhD in weather magic. Once a mage is out of apprenticeship, he might voluntarily put himself under the service of another mage for 5 years for extra class, in exchange of lab time, with new status as he will be considered a fully fledge mage. Some new rules in the peripheral code should frame this kind of study as master and student are in the sanctum of the master, but the student should have more protection than an apprentice.
A "Tradition" is defined by a common belief/perception/understanding of the world as well as a set of supernatural abilities that are "easier" to teach to each member because of their common view of the world - we cannot talk about tradition theory since most of them don't have the equivalent of magical theory. Depending on the tradition, not every member knows all the abilities. And some members have the Gift and some don't. For those without the Gift, they can still learn some Supernatural abilities, but it is much more difficult to acquire them and very unlikely that they will ever been able to use more than a couple (since these abilities are usually Major Virtues).
If you have Subtle Opening, you can technically be initiated in another tradition. However, I don't think it is possible to "pile up" several traditions since "This magus is still penalized for scores in other Supernatural Abilities".
Once a mage has acquired most or enough relevant Supernatural skills as well as a decent knowledge of the tradition, I guess you can consider him as "Opened in another tradition".
At this stage, it is pure speculation since there is nothing in the rules.
However, it is not possible (at least not explicitly possible) to have a gifted person opened in a tradition, then converted to Hermetic magi, unless the original tradition is able to perform its own "Subtle Opening" - it is not a two ways virtue. It is not because Subtle Opening has been integrated in Hermetic theory that any gifted person from any tradition can be converted to Hermetic magic.
I wish I had TMRE in front of me. Or perhaps it is the Hedge Magic book.
I maybe mis-remembering, but I thought the Folk Witches chapter said something about needing to be opened in the Folk Witches Tradition in order to get all the extra advantages/abilities of various Supernatural Virtues.