There's a very simple way to connect them, actually.
The Fall of the Illuminati.
During HR and MD, the Illuminati are pretty much the "Secret Shadowy Cabal of all-powerful figures that rule the world from the shadows."
But by the time the original Deus Ex rolls around, the Illuminati are a rag tag band of old guys hanging on to the few secrets and connections they still possess.
After that you have IW, where the Illuminati recovered a lot of power when the Internet went to shit.
So the only thing missing there is the slow erosion of the Illuminati. There's several ways you can portray this:
>Illuminati as a support column of modern society
You could treat them as an essential cog in the machine, and their enemies start hunting them, on purpose or completely unware that they're actually targeting a secret society.
As the members disappear/die/go bankrupt, societal order that depended on them starts collapsing. Countries go to shit, politics can't do shit, crime skyrockets as the Black Market expands.
>Illuminati as decadent cancer
Very similar to the previous idea, just let some opulent and greedy fucks rule them, and either some of the fringe members get fed up (internal war) or they start attracting attention and get taken out.
On both ideas, you could play as someone from the outside and unveil them, or work for them (unware or knowingly) and plot-twist with the "Illuminate were actually supporting the world because society is a lot more complicated and there's several secret cabals keeping things sane because it servers their interests to keep shit stable".
There's a fuckload other ways to do this, I listed the first one's that came to mind but the point was to use the Fall of the Illuminate to explore what happens when a society is (secretly) dependent on a shadowy cabal and that group goes down. To the neutral observer, this is a good thing (shadowy cabals are bad) and the society collapsed because of… reasons?
To the philosopher, the Cabals (you could have more) have a symbiotic relationship, but as the story progresses, you start seeing it another way: it's a mutual parasitic relationship where both are sucking each other dry and there's no host because all the Cabals and society itself killed them off.
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Low effort shitposts like this should be banned. They don't even qualify as bait and serve no purpose other than to add more vertical space to the thread.