A number of terrorist groups such as the Bloody Hands of Matar, Brothers of Freedom, etc could be considered 'alternative factions' and have enough members running around to claim some kind of independence. The Cult of Tetrimon have survived their banishment long enough to potentially represent a more "evolved" kind of mini-faction due their long period of independence.
There are potential survivor groups, remaining True Citizens or descendants of Immensea for example, either carrying on their legacy or banding together simply to benefit from mutual support in a hostile cluster.
In some cases geographical, political, or other differences make part of an organization (e.g: a colony, a monastery, a station, a division, a department) hold such a greater concern for it's own members and their shared plight than the rest of the organization to effectively make them a faction, institutionalised, rogue, or otherwise.
No doubt there are independent corporations, families, and communities out there making their own way. From the corporation that's looking to dodge empire labour laws by living off the books to the small asteroid colony who bought themselves from their parent corporation and now work as a community surviving on import and export.
There are entire sections of space colonized during the clusters gold rush period, and likely since, that are largely independent of the empires. Leaving endless room for lone colonies on the brink, coalitions between neighbouring worlds, warlords, kingdoms, pirates, and businesses.
Not to mention the myriad places people settle and develop into factions, the cracks in society, the less well administrated worlds, travelling caravans (besides the Thukkers), anywhere that non-mainstream thought can set down roots and form cults, gangs, lobbyists, etc. Even the separation of the upper class of society, or even the ruling class, can lead to them forming their own ideologies that in time become factions.
The possibilities are limited only by your definition of "faction" and your willingness to explore something a little unusual.