Undead.
They don't show up via Detect Thoughts, can't be mind blasted/controlled, can't be turned into more Mind Flayers and eating their brains is a) disgusting and b) ineffective.
Liches are inherently dangerous creatures. There's also fluff about how Mind Flayers prefer using Psionics to Arcane magic because Psionic knowledge gets absorbed by the Elder Brain but Arcane magic does not.
A Dracolich could be pretty fun. Fun aside: Mind Flayers can turn Dragons into Mind Flayers. They become a thing known as a Brainstealer Dragon. The only thing higher up the Illithid hierarchy are the Elder Brains.
Alhoons (also called illithiliches) are Mind Flayer Liches, and are mercilessly hunted down. Most are weaker than the Mind Flayer group, but if one of then went full on Xykon (all those other guys? They were the ones that gave up and died), it could be a problem.
Vampirism does weird things to Mind Flayers. Vampire Mind Flayers are weird feral things. Relatively weak, but if a particularly clever vampire has it in for the Mind Flayers it could be a problem.
"Please - help us. You've got to stop them.
There's some fluff where Mind Flayers are from an Illithid space empire from the future. It was destroyed by an unknown enemy. The ones you see now are the tiny handful of survivors who were thrown back in time by massive spell the casting of which required the destruction of countless Elder Brains. The thing that destroyed them in the future is unknown. Maybe they found it.
Help us - if even if it's only to save yourselves!"
Since Illithids are from the future, it's possible the Illithids discovered the PC's are their ancestors. Or are somehow key to the creation of their lost empire.
Also, the Illithids creep out the Aboleths. The Aboleths are old enough to remember the birth of the gods. They have no memories of Illithids. Maybe they figured out the Illithids secret and are moving to take care of the only thing that will rival them.
Elder Evils is a splatbook all about different ends of the world. Any one of them would be bad for the Illithids. Atropus would be particularly problematic, given that it's the undead abortion of creation itself.
Lords of Madness goes into depth on the Illithids and others (Aboleths, Beholders, Neogi, Grell, Tsochar) and is probably relevant to your interests.