A major breakthrough based on the Shapeshifter Virtue and similar Virtues and Flaws could lead to:
Hermetic shapeshifting, minor (Hermetic) Virtue
Your deep understanding of shapeshifting allows you to create Muto spells and enchantments that, when affecting a target possessing the Shapeshifter Virtue (or a similar Virtue or Flaw that allows it to change in such a way that the end result is non-magical), on expiration leave the target in the current state rather than have it revert to its original state. This Virtue pushes the Essential Nature limit, but does not quite break it because it exploits the essential mutability of these targets.
In my saga, this is the minor Hermetic Virtue of ex-miscellanea shapeshifters, and synergizes well with their Major Supernatural Virtue, which is obviously Shapeshifter. It is inspired by (and balanced against) the Sense of the Mystic breakthrough in HMRE.
While that's a fine virtue, I would argue that the very fact that it's based on the Shapeshifter Virtues and flaws would mean that it's Integration, rather than Original Research. You can, of course do Original Research which duplicates an Integration, but in terms of game mechanics you'd probably be better off just going out and studying with a Hedge Witch or three for a few seasons.
Out of all of the Supernatural Virtues in the core book, the Shapeshifter virtue is the one I look at most and think "why the heck hasn't some bonisagus already had a Hermetic Breakthrough with this?" I mean, they're all over the freakin' Black Forest. Of course, I can No-Prize myself out of that scenario: political pushback from Bjorner, the general case of the Order just coming out of its own Dark Age due to the Schism war, it's not sexy enough for the lab rats, Maybe they HAVE but just haven't gotten around to fully publishing, etc. Still. It's a direct example of a flaw in Bonisagus' theory. You'd think they would have at least gotten SOMEWHERE with it.
I'm definitely on board with "it's not sexy enough for the lab rats" and "it's a bloody Hermetic Breakthrough, and nobody since Bonisagus has ever managed to actually break the Limits." A Hermetic Breakthrough, for anyone who doesn't have Bonisagus' level of plot behind him, is not only a lifetime project but an unlikely one to succeed, and shapeshifting is a rather pagan and silly ability that a lot of Bonisagi would look at as not worthy of trying for a breakthrough on that level.
Now pardon me while I go back to studying under that paranoid Mythic Alchemist and trying to steal the secret of matter transmutation...
IMHO, I would not require a Breakthrough, or at most only a minor one (15 points).
I would probably go with a Perdo spell with a duration: it dissipates part of the destructive power of the attack. It should work against anything where it is possible to decrease the intensity of the attack (fire, lightning bolt)
Now looking at it, because it is a Perdo spell with a duration, a minor Breakthrough make sense.
For other effects like physical attack from weapon, destroying the kinetic power is not really within paradigm I believe, so Perdo should not be the way, but probably Rego to slow down the blow/hit, effecitvely reducing the damage sustained. This effect should not require a breakthrough: there are already spells holding person & item in place, this effect is just slightly less efficient since it does not freeze them.
It's part of Euclidean geometry, although Plato's Seventh Letter gives a detailed explanation of a circle. He explains the perfect circle therein, and describes how it is different from any other drawing or words.
But this does raise the question: just because a circle is perfect, why does that mean every other polygon or shape isn't? Geometers have existed almost as long as mathematics has, and they've long studied other natural and unnatural shapes to gain a better understanding of the world around them. Why couldn't someone have a breakthrough with other shapes if they followed some of the teachings of these geometers?
Well, there's already a Mystery of Hermetic Geometry that works with regular shapes (though a "circle" target already works with "close enough to circular"). So I imagine that another shape as a target would be a Minor Breakthrough. The reason people use circles is because they always have, and because nobody's really found a use for another shape (though I could see someone wanting to do something with triangles or pentagons).
I could put this one in the same category as "duration: ring" - in the sense that it's variable, but can be physically interrupted with a simple activity (ie, disrupting the ring/smashing the cogwheel). The disadvantage is that unlike a Ring, it's much more difficult to make a REALLY long-term effect. However, it's probably more difficult to casually disrupt. (You have to physically break something, rather than just swipe your foot across a line.) Of course that's dependent on how you define "break a circle", of course...
A research to allow magi to do multiple projects of different Te/Fo combinations at the same time would be nice. It's already possible through teaching spells to other magi, but it would be nice if it was extended to inventing spells, inventing from a text, or enchanting objects. Sometimes you want to do several small projects.
Probably you'd be limited to your lowest Te/Fo combo and compare all wanted effect against that.
Aegis of the Hearth as a Circle/Ring duration would be amusing - mainly for the (minor) impact to Hermetic society that would result.
EDIT - actually, even just a single Breakthrough project of this - a lvl 20 version, for example - would be highly useful for starting covenants, and could probably be a meta-game justification for not worrying about getting the Aegis re-cast every year. Although it does assume that "breaking a circle" is significantly more difficult than just drawing a line over the circle itself, I suppose.
I disagree that a minor breakthrough is needed. Inventing a formulaic spell can vary the traditional R, D,T parameters, so I'd see a spell specifically developed to use a "square" D:Ring as being essentially the same. Just my 2c.
A Hermetic Breakthrough achieves a minor impact on Hermetic society? Changing the parameters of Aegis is a Hermetic Breakthrough. So, if one is going for a different Duration, why not also change the Target, too? Yes, two Hermetic Breakthrough's now, but now you have a spell that can be cast in the field of battle in moments rather than hours AND may no longer be a ritual spell. I say may no longer, because it's unclear if the reason for the Aegis being a ritual is because of it's Target and Duration, or the power of the spell. My guess is that Aegis being a ritual has to do with Target and Duration.
Well, some breakthroughs are in fact kind of minor (disproportionate to the effort put into getting them). Bending the Limit of Arcane Connections to allow Voice-range at unsensed targets, for example, is one of those things that would look flashy and get you put on the fast track to Primus Bonisagus, but I doubt that its implementation would be entirely world-changing. Neat trick, and a patch to a flaw in Bonisagus' theory, but it's a rather less massive change than "hi, I just integrated vis-less rituals and am now using permanent Creo right and left."
Anyway, I definitely think that a Circle/Ring Parma would be pretty useful for magical combat (though with obvious disadvantages; you have to draw the circle and aren't going to move around while defended). An unrestricted Parma effect in Rego Vim...yeah, that'll shake the Order, or at least make Invisible Sling of Vilano a very popular effect.
A hermetic breakthrough could be to break the lesser limit of Vis and allow changing the attunement of vis. Of course there has to be limits on how much you can transfer and also some form of transfer-fee.
For minor breakthroughs there are several virtues that can be researched as spell mastery options. Hood examples are Life Boost and Flexible formoulaic Magic.