Aegis Research apparently doesn't have a home system, at least according to EDDB. So that means, at least theoretically, a dedicated enough player base "should" be able to cause them to retreat from all the systems they have presence in, right? There's a couple systems they're in with only 4 minor factions though, so I'm not sure if a retreat from those would be possible.
4 you can get a Retreat from still. 3 you can't [1].
They will have a home system - there's no in-game way to determine it, so EDDB just doesn't record it where it's not known. It's not completely impossible that it's not one of the systems they're actually in ... but Frontier have been tidying up that sort of thing recently so I would guess that's not the case this time.
If it is, though, pushing them out of all their systems is possible ... and will cause them to reappear instantly in whatever their real home system is. Of course, if that's something like Polaris, or Col 70 something, it might take a while to find them again.
[1] To be very picky, you need at least 4 factions to get a
Pending Retreat. Once you've got that the Retreat itself can still happen even if another faction leaves the system in the meantime.