I'd like to enlist the whole community for a project I think would have some value:
Many of the alternative magical tradition books, Hedge Magic, Rival Magic, Cradle & Crescent, Book of Sand and Sea, Mythic Locations, etc have official suggestions for different types of breakthroughs for hermetic magi to integrate. However, upon close reading of the text, and I think this is intentional, one can find many other more subtle examples not spelled out.
This thread is for such implicit examples.
I have now updated this thread (again, Jan 18th, 2019) with what others have provided and a bit more of my own research.
1.) Animo as a Hermetic Ability (Hermetic)
1.) Vis-less enchantments
1.) Everything? No breakthroughs are explicitly stated at all.
2.) Storms move with the Magus (Minor)
3.) A magus is immune to the effects of their storm (Minor)
4.) Grant temporary Confidence points (Hermetic)
5.) Nullify botch dice in the future (Hermetic)
6.) Reroll a failed or botched die roll in the future (Hermetic)
7.) Inflict botch dice on an enemy (Hermetic)
8.) Force a target to roll a stress die instead of a simple (Hermetic)
9.) Force a target to roll two dice and take the lower result (Hermetic)
10.) Revivify a Corpse, order it, question it, (Major or Hermetic)
Sahir of the Cradle and the Crescent:
1.) Limit of Time (Hermetic Breakthrough): Solomnic Astrology can see into the future, and divine the past.
2.) Limit of Aging ( or Hermetic): Sahir using a spirit can reduce their age through the Elixer of LIfe, it does have side effects however such as lost memories and XP. They also can remove aging points, but not decrepitude.
3a.) Directly Travel to the Magic or Faerie Realms (Major): Sahir can cast ritual spells to open portals to these realms. May or more may not include opening "Windows" into these realms to scry.
3b.) Directly Travel to the Magic Realm (Minor):Sahir can cast ritual spells to open portals to this realm. May or more may not include opening "Windows" to scry
4.) Corpus score giving a bonus to aging rolls. (Major)
5.) Convert Sihr into a Hermetic Virtue (Hermetic)
6.) Hermetic Item Empowerment with spirits (Major) (also see The Mysteries Revised Edition)
7.) Spirit Familiar (Major) (also see The Mysteries Revised Edition)
8.) Hermetic Dream Travel (Hermetic) (also see The Mysteries Revised Edition)
9.) Hermetic Thuergy (Major) (also see The Mysteries Revised Edition)
10.) Restore Fatigue (Hermetic)
11.) Restore Might to a supernatural creature (Major)
12.) True matter transmutation (Hermetic Breakthrough): Mythic Alchemy is not bound by the Limit of Essential Nature. (It's entirely possible that this cannot be duplicated; the inventors of alchemy were a Divine tradition after all...).
13.) Accelerated Experimental Philosophy (Hermetic, possibly Major Breakthrough): Solomonic Alchemy can do what Experimental Philosophy alchemy formulae, such as matter purification, can do in a single spell, which is either Rego-crafting without Finesse (not a Hermetic Limit, but a severe limitation of Rego's function) or Creo-transmutation without a ritual (Limit of Creation).
14.) vis-less Permanent effects from formulaic spells - see Erik Dahl's comment in https://forum.atlas-games.com/t/new-herbam-and-other-spells/157/1
1.) Target(the Gift, or magical virtue) (Minor)
2.) Duration: Action (Minor)
3.) Target: Journey (Minor)
4.) Reduce Distance between two points (while travelling): (Major)
5.) Inflict Flaw, (Ability Block), (Major)
6.) Base effect: Target can't spend confidence points (Major)
7.) Base effect: Target suffers botch dice when attempting a particular activity (Major or Minor?)
Sorcerers of Soqotra:
1.) Faerie Enslavement
2.) Dispel Magic by Group (Same Art or Supernatural Effect)
3.) Remove Flaws that the character has gained (Hermetic)
4.) Restore lost virtues (Hermetic)
5.) Cure wounds, regrow limbs, and halt physical ailments without Vis (Duration: Regrowth) (Hermetic)
6.) Repair objects without vis (Duration: Regrowth) (Hermetic)
7.) Which ultimately implies, creating things without vis (Hermetic)
8.) Grant Virtues and Flaws (Hermetic)