I've been thinking about progress in the order. Although the medieval idea of progress isn't like ours, its clear that the mages have gone from a system that was terrible (pre-order) where magi just gunned each other dead in the streets to steal their stuff, to collegiate. Now magi get more out of sharing. Those books can be traded for instead which means everyone benefits.
Likewise, although slow, hermetic magi does grow. Bonisagus magi are constantly working on breakthroughs and integration of non-hermetic magic is a thing. Its entirely possible that over a 150 year lifespan, a magus will see the introduction of several new ways of doing hermetic magic that simply weren't available when they gauntleted.
Given this, its clear that magi should have a better concept of progress. They know their own history and can see how things change and improve for the better.
Now picture a young, talented (int 5), Inventive genius. He wants to move the order on to be bigger, better and stronger than it is.
Where would you start?
The obvious starting places for me are
Sharing of very high quality books to all covenants, ensuring that freshly gauntleted magi are studying from the best quality sources and advancing much faster in their arts. This is also mechanically easy to do. Well trained scribes can do this without the intervention of the magi and its not impossible to imagine a well funded covenant employing dozens of such scribes in an almost monastic environment to produce such tomes in bulk.
Integration of non-hermetic magic and hermetic breakthroughs. These are the only real ways to expand the scope of hermetic magic but are hard to do if done by a single magus. The only way to do this more rapidly is to get teams of magi working together, sharing notes and running different experiments on the same project. This doesn't mean lab sharing or other such demeaning work, rather working parallel on the same problem. For hermetic integration, you'd need not just the lab teams, but also organised teams of seekers to find the sources from which to work.
Vis distribution. Vis sources are randomly distributed meaning that some covenants are stockpiling vis they aren't using and others are crying out for vis they don't produce. There are two ways around this, a better vis distribution system and hermetic alchemy. Alchemy is the province of mystery cults but has the capacity to dramatically change hermetic vis production entirely, especially the virtues hermetic alchemy and major philosophic alchemy. This lets magi create vis of any art, right out of their aura without committing any extra time to it (beyond time they would spend in their lab anyway)
Hermetic numbers. Hermetic numbers are limited by two things, vis supply and gifted children supply. The vis supply is because every extra mage is a competitor for a limited fund of vis, although, see above for how to address this. The gifted child supply could be addressed by non-gifted grogs dispatched to population areas bearing magic items that detect the gift (using the guidelines in Apprentices). With an abundance of gifted children, Magi could be a little more picky about who they train, probably leading to an increase in the quality of young magi. With better quality libraries and an element of self directed study, assisted by mortal tutors, you could even have multiple apprentices at once, although their safety would really depend on changes to the code.
Magical Infrastructure. Moving vis, books, gifted kids, magical animals, lab equipment, specialised components and ingredients and so on around is currently done on an individual covenant to covenant basis or by redcaps. Redcaps are few in number and travel light and fast. Moving a book or a rook of vis is no problem, but moving fresh venentian glass for 5 labs requires something else. There is considerable scope here for an enterprising covenant to develop a system of distribution while setting themselves up as a manufacturer of goods, such as glass, fine quality steel tools, particular herbs etc, and hermetic magic can help in the production of these to standards far higher than normal mortals can aspire. This would allow magi to address deficiencies in libraries and vis stocks swiftly and maintain better quality labs.
Almost all of these changes are not mechanically difficult, not like erecting networks of Hermes Gates. The great stumbling block is social. Many of them work directly against the prevailing mindset of magi and how they view themselves. Some of them even work against the code (such as having multiple apprentices). So a magus or covenant wanting to really move the Order as a whole forward, would need to think carefully about how they would change the culture and the legal framework of the order. The legal framework after all was created to be acceptable to fiercely independent magi who would otherwise be murdering each other and taking each other stuff. Arguably, and Tytalus aside, the order might be ready for some provisions, if only in local peripheral codes, that move towards a more collegiate atmosphere.
Magi would also need to have their mindsets changed. Perhaps the best way would be to create some of these changes between what willing partners could be found and offer them to others with a oath of reciprocity, i.e. you can get the benefits of using the new book system, but to join the scheme you have to open your library to all other members of the scheme, as they have opened their library to you. This in turn would require enforcement for those trying to cheat the system (Tytalus again) and perhaps some peripheral code rulings.
An in game example of how this could be developed already exists in the Theban tribunal, where magi are well used to coming together to form leagues with a particular purpose. These could certainly be practical for research groups and could be expanded out more broadly to the other provisions.
The aim of all of this would be more powerful magic, and thats a good sell to other magi. Join this system, and you'll get access to all the best books, all the vis you need for your projects, multiple quality apprentices and great lab equipment.