So, I've been thinking a little about this, and I think I've found a way to reconcile both arthur's concern and my preferences, above, in a satisfying way.
Arthur, should this be a game-related question, I hope this will be of some use to you.
So, we start with these:
- Initiations would be very interesting for the House
- Mystery Cults are not tolerated and / or don't accept tremere (yeah, "tremere are evil" trope sucks)
- So the house would need its own set of initiations
- But there's no Tremere MC cult.
First, to be clear: I wouldn't use Organization Lore: House Tremere for any of this. This would, effectively, turn Tremere into a MC house, and make it too easy, especially in regard to magi who will have to, for exemple, increase their Green Cockerel Lore.
But I would make knowledge of the following a secret requiring a level of HT lore to be aware of, and considered. Say, HT 3, but YMMV.
For a long time, the house either thought that the only MCs were the MC houses, or that you couldn't get a secular MC.
This all changed somewhat recently.
Alternative 1: This changed when the house learned rumors about Fortunata building her own secular MC
Alternative 2: This changed when a Tremere PC, having played through the Fortunata adventure, brought new insight to the House.
So they decided to do just that: Create a new, secular MC within the house. Say, on the pattern I modeled above.
Call it, I dunno, Specialists Lore.
But either it's been too recent to have much progress, or, the house's resources not being infinite, they couldn't divest enough to make much headway.
So there would be very few books / teachers on this new lore, and they would have a low skill level. Likewise, I'd limit initiations on some, or all, of the Curious Common Magics
Alternative: This is all new, and starts with the PC
Now, how to insert your players into this?
Well, look at them and their interests.
If your PC is the lab rat type, he's tasked to do original research, write books, integrate scripts, develop paths, this sort of thing. Tremere NPC either work on the same project, or are out there searching for lore, meaning you get to add points on the project whenever you want it to advance and have the house feel powerful. Like "Bonisagi may to a lot more research on the whole, but we are focused and efficient".
This also allows you to somewhat shift the project, by making certain virtues easy to get (lots of progress by NPCs) or by giving the PC help from other magi while self-initiating.
If your PC is the adventurer type, she's out there, searching for insight sources or ancient magic. Maybe she's being exploring ancient crypts for ancient scrypts, or stealing from edge wizards, you get the idea.
This would be a welcome place to repurpose Fortunata's island (raid her note to improve Specialists Lore, gain help in integrating initiation scripts, that sort of things).
As a member of the vexillation, she'd be initiated by the lead researcher.
If the player just wants some initiations, he may be tasked, as an exception, to join an existing cult, learn everything that he can, and bring it to the House.
This way, you have an excuse for this player getting initiated without other tremere being.
You can vary the degree of paranoia and distrust in the cults, from "No one knows anything about other members, so it's easy to not display being a tremere" to "they are ultra-paranoid and check everything" by way of "they don't care, and laugh at house tremere".
If your player likes this kind of stories, this is a great way to play on conflicted loyalties (especially if an initiation inflicts a suitable flaw), friendship, suspicion, fear of discovery... You could milk the hell out of some spy thrillers here.
Alternative: On a thriller mode, I can see a character "leaving" or "being expelled" from house tremere in order to more easily join a cult. They may even openly be on good relationship, explaining the character's frequent dealing with the house, with a cover story of "They had a deal to make it seem all cozy as part of a PR effort by house tremere, but the truth is that, secretly, the House resent the PC and would rather get rid of him"