I don't like to use the term "ASB" lightly but I fear it must apply here. You've covered that with your "illuminati" reference, not to mention hints of vampires

; but I think that's what it takes so you really should have launched this in that forum.
Mere human beings probably cannot maintain some Mason-esque conspiracy (going by what the alarmist opponents of Masonism luridly believed, not by what Masons really were and are OTL) as a coherent plot going generation after generation. Also, just what is their motivation, even assuming they can possibly maintain discipline?
Put mystical immortal beings into the mix and we might be going somewhere. Alien Star-Trekesque "energy beings" might fit the bill, or of course your vampires somewhere on the Anne Rice/Buffyverse spectrum.
Buffyverse vampires can't be arsed to organize themselves as a world-conquering conspiracy; check out the last episode of Buffy Season 2 for Spike's reasoning plus the demonstration of his deeds versus Angel's--vampires who identify strongly with their demon side want to simply end the human world and if they get grandiose enough to organize under that rubric, that's the nature of their conspiracy--have some mega-demon rise up and swallow it or burn down all the "righteous" humans or some such; vampires like Spike who rather enjoy parasitizing on our world don't want the responsibility of messing with it. They just like to skim the bloody cream.
They just aren't much for organization.
So I suppose any vampires involved are either quite different from Buffy-Verse or are along for the thrilling ride, not the kingpins of the organization.
Given that there are shadowy forces at work unknown to the common man, the question arises, why didn't they take over long ago and rule the world openly to this very day? In Buffy-Verse the Slayer is a short and partial answer, but it seems to me there there are deeper principles at work, of which the Slayer line is just one manifestation. Sort of ecological. Our Earth is moving away from the demon origins, demons stay in contact with it but on the whole from their point of view it's a corrupt and slummy backwater, working out its new destiny. (Cue Angel in the last ep of that series--"the humans are winning." Here anyway.) The failures of various human organizations that attempt to mix otherworldly powers with human ones (the end of the Council, the failure of the Initiative) indicate that there's something flawed in their program that dooms them; I think it's because they are bucking the trend of Earth to move off in its own humanistic direction. The deep reasons for this are buried in mystery in the Buffyverse.
In other mythos, like Lovecraft, it's just the cyclic nature of time--the Old Ones will be back and we can't stop it, any more than they could prevail unbroken through our mundane interregnum.
Others will posit some epic battle going on the larger cosmos, of which we are just footsoldiers; in that view, this conspiracy is taking a side and presumably the other side will counter with its own reactions and initiatives.
If we can shed the whole ASB business of unknown mystical forces at work, the challenge is to come up with some realistic human organization that can do the job, one I've already dismissed to my personal satisfaction though I'll applaud anyone who can pull it off convincingly.
If we are going to have mystical stuff (or aliens with tech sufficiently advanced to be indistinguishable from magic, or conceivably aliens with tech and agendas we can sort of grasp and try to outguess) we have to be specific; state the boundaries of their capabilities and their goals.
It could be there's a mystical background that is in itself neutral in terms of human history, that human historical actors learn of and seek to harness. If we have some kind of magic (including manipulating neutral alien tech left lying around) in human hands, I suppose some aspects of it might overcome the tendencies of any human organization to drift off on various tangents. Say it involves some kind of immortality for key members of the inner circle, so some gang of wizards (POD implies they don't get their act together until the 17th century, so that's the starting point) from Jacobean times is still running the show. Or they can compel people to stick to the program by swearing them to mystically binding oaths that destroy those who stray from the path.
Frankly if they have powers like that, I suspect that long before the goal is achieved they come up from underground; securing unchallenged power in some stronghold they systematically go about conquering the world openly, confident their opponents can't match their powers even if everyone outside their domain (and many dissidents within it) unite in determination to stop them.
But you still have to specify the parameters of their special powers. These might cleverly explain why they remain secretive even to this day.