(GURPS Magical Styles: Dungeon Magic, p. 6)
This style fits without much tweaking for my gameworld. I don't see anything in it which would forbid it from being a sanctioned Brotherhood style. I could even see the fairly radical members of the school accepting female members in a direct violation of the Brotherhood tenets. I already have style that's part of the Brotherhood, the Fraternity of Gideon, that does so. It certainly wouldn't make them popular, and I imagine few Fluidists would hold office in any guilds. It strikes me that the last thing a Fluidist would want that sort of responsibility, anyway.
The Guild of Iron Mages
(GURPS Magical Styles: Dungeon Magic, p. 10)
The Iron Mages fit in well, with few changes needed. As a conservative style, I don't think they'd support female members, so they'd certainly be a Brotherhood school. In my opinion they need Enchant and some Weapon and Armor Enchantments added to their spell list. I don't run straight Dungeon Fantasy and those are spells it seems like they should have even if PCs never use them.
The Old School
(GURPS Magical Styles: Dungeon Magic, p. 13)
Necromancy is one of the big no-nos in my gameworld, and is illegal almost anywhere. However, I think that unlike the Onyx Path the Old School could work as a Brotherhood school of licensed Necromancers, especially since is says in their description they fight that identification. They wouldn't be able to wander around in public with a gaggle of Zombies but they could get away with a lot just from being official.
The Order of the Sun
(GURPS Magical Styles: Dungeon Magic, p. 17)
Straightforward boom-boom mages? Sure, why not? I don't see anything that makes me hesitate in throwing this bunch in. It seems like the sort of group that wouldn't necessarily seek to be a part of the Brotherhood as a whole school. Certain teachers might be, but there's room for those who aren't. They don't teach anything that's treated as Black Magic and are often Impulsive and Overconfident, which says to me they're too erratic for the Brotherhood to try to control them all. Plus, when an orphanage gets burned down by a misplaced Blast Ball the Brotherhood could then say "Not our fault!"
The Sisters and Brothers of Echoes
(GURPS Magical Styles: Dungeon Magic, p. 20)
I'd use this style as it is, and since it readily accepts women it's not a Brotherhood school. They teach Mind-Search, which skirts the edges of Black Magic, so the Brotherhood might try to run them off on occasion, but they know enough useful spells, and they practice their magic in a public enough manner, that secular officials probably allow them to practice magic in spite of the Brotherhood's distaste. The Brotherhood isn't absolutely powerful and I think it's a good thing for there to be reminders like this school scattered about.
The Tower of Pentacles
(GURPS Magical Styles: Dungeon Magic, p. 24)
Another school that fits right in. This would definitely be a Brotherhood style. They strike me as filling a need for judges and negotiators within the Brotherhood, and they are respected enough that their ties to the Echoists would be overlooked. For that matter the Pentaclists probably have enough pull that they're the reason the Echoists continue to exist outside the Brotherhood framework.
The Wizards of the Mirrored Gaze
(GURPS Magical Styles: Dungeon Magic, p. 29)
The Bene Gesserit... I mean the Wizards of the Mirrored Gaze fit in great with a few adjustments. Firstly, they're now the Sisters of the Mirrored Gaze and are female-only. They get around the legal prohibitions against female mages by claiming to be a religious sisterhood, they're just vague about the gods they serve. They have a number of spells that politically powerful people would find useful, so I think they'd often be found among the connected, and could use this to guarantee their continued existence. They definitely know spells that qualify as Black Magic on my gameworld but since they cast them for the right people they can probably get away with it. For a while, anyway, as I could see a King Philip vs. the Templars situation happening if the Sisters aren't careful or get too rich too quickly.