I'm sort of curious though - if you were to make five (or so) Al-Quadim meta-factions what would they be?
Personally, I'm tempted to keep the Emerald Enclave as is (maybe change the associated color/gem).
Then go with a sort of Scrivener organization with both explicitly religious (preserving and finding tales of the Loregiver) and arcane (keeping control/hidden texts on the Elemental Blasphemies and transported kingdoms) goals.
A humble order with the explicit mission of keeping pilgrimage routes open particularly through/during periods of political unrest. Maybe name them the Gatekeepers or Warders and have a backstory of them being the successors to the lone humble official who kept true to the duties of the court during a disruption in the succession of the Caliphate. Membership is lose, consisting of only some vows, call-signs, and an obligation to gather in secretly marked caravansaries and sheltering caves from time to time. It's an unusual organization in that it counts both the most decorated and dedicated Faris, Ethoists, and Janissaries among its ranks as well as Beggars, Barbers, Mystics, and even the occasional out-caste or Ma'trud.
The Glorious Network of Pearls and Steel - originally a geographically diverse political alliance devoted to a formal ties between the Pearl Cities and Hiyal as a counter to perceived threats of influence, commerce, and culture from the Pantheist league, it has since turned into something - else. While still, in theory, devoted to the advancement of these original cities, it has become, in fact, a network devoted entirely to the advancement of its members and those they patronize. The network has a strong and controversial public face - a political leader in need of attention has little better option than to alternately embrace and castigate the network; its policy of selling to 'the unfairly maligned'; opulence/artistic patronage; and willingness to set up missions/fortresses in the most remote locations with very little oversight.
Now the 5th faction is supposed to be the Lord's Alliance - a sort of Pragmatic Law & Order Network - but that doesn't really make sense to me in a Zhakaran context, so I'm tempted to go with something... stranger and make it the 'Zhent' analog. Maybe a network with connections to the Yak-men, Ghuls, a cabal of giants and hags, an manipulation-based specialized djinni, mad mystic, the Zhakaran fae, a rogue faction of enlightened beasts, or even the remnants of a pre-Loregiver Drow community. With the idea being that this group isn't something one belongs to - necessarily - but is one that one might owe obligations to or find oneself supported by and that while that support might be strange and their motives inscrutable their actual actions are frequently supportable - for whatever reason, they don't like disruption. Their plans within plans require stability, their aid (while infrequent) is telling, and the only string attached is that you keep being you and don't think it through.
Alternately - I could go with something like 'The Captain's Alliance' and instead of having it be princes and tycoons, make it sheikhs, free company captains, and privateers. Let it play off of the 'three peoples' theme for Zhakara and have it be an explicitly adventuring organization. When you are a member you are largely one among respected, semi-powerful equals. The catch being, they are actually serious about doing what they ask you do to (as an adventurer) and that while their immediate goals (independence, cooperation, helping out with major potential disasters) are nice the actual world they want (weak political powers, plenty of opportunity to make money out of conflict, chaotic frontiers, independent rather than integrated communities) may not be that great.
I'd also be tempted to do something with the Pantheists - just because they are a nice bit of color and do seem like they would sponsor or have a meta-organization out and about, but... I feel like maybe that works better on a more character based level? After all, it's hard to picture them getting interested in something and not have it turn geo-political pretty fast. It also feels like making a character with Pantheist ties is a great resource, but asking a character to join a Pantheist organization seems limiting.
Then Again:
I'm also tempted to do a Zhakaran version of 13th Ages Icons, and while I think the two systems could coexist profitably, that's extra work on a project where I'm already taking on a lot.