One of the main things I'm unsure about is how to have "interest groups" ask for things that actually make sense and aren't annoying...
...It's not clear to me that there's actually much for Interest Groups to actually ask the player to do, so I'm not really sure how to solve that problem.
Faction Issues could be expanded as a quest system, where right now each faction has 1-10 Issues which are just a bunch of yes/no objectives.
These could be replaced by random anomaly like events which give several mutually exclusive decisions with varying rewards and outcomes in favour of one faction at the loss of another; some rewards being worth angering your primary faction and elevating their opposite.
Examples:
-Pacifist mining faction wants you to colonize x world for its riches and will start the colony with several free districts, but it's a tomb world and you are a spiritualist.
-Stolen/abandoned tech or equipment from a planet in your territory to distribute amongst your factions
-Militarist wants you to declare war on x target
-a faction wants b tech, x faction wants y tech from your current pool
-spend x resource to receive a reward from y faction
-event chain to establish Holy Worlds(should not be an AP or manually selected imo)
-more event chains like the Rebel Shipyard/Flagship that can spawn dynamically based on things like the number of unhappy pops in a given faction in a particular sector.
-interactions with leviathans, space critters, neighbouring empires
As long as they aren't too intrusive with pop ups and reward "normal" gameplay I wouldn't mind some short or long term objectives to do in the early/mid game.
That is on top of the fact just about every single election or leader/ruler change, policy, civic, edict, event, anomaly, or dig site in the game could have the choices affect x or y faction approval. Right now factions are almost completely isolated from the rest of the game and only affected by ethics attraction which is pretty indirect.
Factions and these "interest groups" I feel are also in the same field as the Institutions, Religions, and Cults which
@grekulf mentioned in
Dev Diary #141 and could share similar mechanics.