It used to be possible, but they "fixed" it so this is now no longer the case. "Exiled" factions were restored to presence in their home systems.
Evidence: not long after I started playing (it would have been in version 1.4), the "Traditional LP 245-17 Law Party" was no longer present in the LP 245-17 system; they'd been exiled to Hecate. I only found this out when I acquired a bounty ticket for them, and some time later I went to LP 245-17 to claim it, only to find they were no longer there.
But now I see the TL2LP is not only back "home", but is now in control of every installation there, according to Inara.cz.