After the ones I mentioned, I added the Unity of the Brethren as a kind of catch-all for clandestine Protestant organizations across Europe. Afterward, I added a kind of generalized "Sufi Orders" society with the implication that any player who picks this would select an order for themselves, and a society titled "The Scientists of Europe" representing the interconnected web of early modern alchemists, astronomers, physicists, and various other early scientists. Would've just used the Royal Society, but it's about 32 years too early for that
Why not call it the
Invisible College? It's more a conceit than a real institution, but if you want a secret society of scholars, it fits well. 1628 even comes a mere 3-4 years after the masque that inspired it, meaning the players could even be founders. First time actually meeting in 1645? Pish posh, that's just the cover story. ^_^
But otherwise, there's the
Académie française, or for players in Italy,
the brigata dei Crusconi.
EDIT:
I was also thinking, if the players operate in the Mediterranean (probable, given Sufi orders), you could include the Knights Hospitaller and the Barbary corsairs as opposing elements. This is the era in which the Barbary states are at their peak, after all, and their membership includes Muslims, Sephardic Jews, and even Christians, slave-taking, raiding, and generally kicking the European powers as much as they can. Along the same token, the Netherlands are still young and still fighting for their independence - the Watergeuzen are a perfectly viable option. Any of the Venetian houses are viable options; trade, intrigue, and gold abound in the City of St. Mark.
If this is more Baltic than Mediterranean, the Hanseatic League, while weakened badly by the Reformation, still technically exists, and its legacy will stretch on even after its last formal meeting in 1669. Here, the Dunkirkers are also running around, causing trouble in the North Sea and Channel.