I presume that philosophy could not work as well or better as such, or it would be going on already. But why couldn't it? I'm sure there are good reasons I can't think of. But those not in the business like myself wouldn't be able to apprehend them.
The pie in the sky that's partly to blame for obscuring my thinking on this point. . .
I imagine an online "hub," analogous to existing software hubs (which I only have a quickly passing acquaintance with), where people form groups, establish axioms from seminal works perhaps including some of their own, and then go on to establish propositions with proofs. At every step of the way, a graph-theoretic graph of the system in its present state is pictorially viewable at any zoom level or through any filter that extracts graph paths. A node would represent an axiom or a proposition with a proof, any of them possibly accompanied by secondary items in their own directories.
The 3D moderately interactive models wouldn't be an essential feature. We just assume it's a feature in our imaginary hub to try to help one indulge the intuition with me if needed. If you don't need it or find nothing to indulge, the question probably ends here or before here for you.
At any given point, "[System Name] Orthodoxy" would be all the accepted supporting literature plus what the group has established themselves. New nodes (directories, each of which contains a proof with a bibliography along with perhaps copies of the supporting literature) would be either incorporated or pending incorporation, if not outright rejected. Further new nodes may be derived from nodes pending incorporation (or from a combination of pending and incorporated nodes), but their future status depends completely on the status of its weakest parent (if it's not eventually just ordered for deletion).
Deep self-modification may always follow as a group (which may involve some social hierarchy), such as adding axioms, and modifying or deleting axioms and making sure the changes propagate. The group may merge with another group. All of this, except maybe the adding of axioms, could be a lot of additional work – but no one assumes that philosophical reorganization and development isn't without end (especially if it's receiving possibly another cue of the relevant kind from pure mathematics).
There would be casual and less casual discussion areas separate from the orthodoxy.
You get the idea.
Hopefully. I can also already imagine minor technical complications to the idea (the implementation not being important here), but the ones I'm coming up with also have equally mundane solutions and plead not be invoked as red herrings. For example, "External literature would apparently defeat the point." And to this an answer could be that external literature would serve as records of the "dirtier" or "poetic" thought processes that inspired a new proof or serve as a continued source of income for the journals and those who can sell their works, among other purposes similar and disparate.
If observed from the outside there would sometimes be seen a lot of similarity among groups. This would be a positive aspect. Given that no one could be in more than one group at a time and that anyone can start a group, anyone with internet access could find a philosophical system she fully and clearly identifies with at its current state and can become part of its group and environment either as an observer initially or as an accepted participant – not much different to how the sociology already works anyway.
Perhaps this way, as one substantial improvement to the domain of philosophy, people can be much clearer on what all they believe and what all others believe. There would perhaps be somewhat fewer drawn-out impasses, less apologetics, more substantive production. Someone could just give you a link to their system or a link to a graph walk portraying their current specialized focus (accompanied by its overall acceptance status in its family). Maybe stronger thinking or a fresh morning mind could've elaborated much more or elicited additional reasons in favor.