To learn a hermetic virtue, the best way is to be initiated on a mystery. And this way allows to learn some Major Hermetic (like Mercurian Magic, Hermetic Rune Magic, some Major Focus,...)
But yes, following the book Apprentices, you can teach Hermetic virtue to your apprentice. Just be aware for the difficult :
Need : 21 in one season for a Major Virtue. malus of 9 on the teaching score by Major Hermetic virtue; malus of 3 on the teaching score by Minor Hermetic virtue
For instance, Tethys ex-Tytalus, one of my character. Elementalist (Major hermetic virtue), puissant Aquam, puissant Auram, inventive genius, study bonus (4 minor hermetic virtues)
communication + teaching + 3 + 6 (one-to-one) - 9 (major hermetic virtue) -12 (3*4 hermetic minor virtue) >= 21
If his parens wanted teach her a Major Virtue, his score communication + teaching needs to be up to 33... With a major flaw and good teacher, the score would be reach to 19.
For a Minor virtue, the score would reach to 13... in the best way.
Other case. Sileken ex-Miscellenia, another of my magae. She had only faerie-raised magic as virtue. If her parens would have taught her a second Hermetic virtue :
communication + teaching + 3 + 6 (one-to-one) - 9 (major virtue) > 21
The score communication + teaching must be 21... 16 with good teacher; 7 with good teacher and a major flaw.
So yes, it's possible to teach a second Major Hermetic outside the mystery, with the good conditions. But, it's really complex. A third would take some seasons to do.