After seeing pathers and pirates eternally popping up on the fringes, seeing core worlds destabilize and never come back, finding ruins out in deep space where no one goes, and finding beautiful spots to build out in the far reaches of the universe I started to see a possible way to add some spice to the sector at large.
Let the Major Factions Grow and Die
If there are worlds near a major faction's territory that have a good value, let them claim those worlds slowly over time. If they have industries that are losing them money, let them remove those industries. If they could add an industry that would improve their worlds revenue then let them add it.
If their worlds aren't making enough money, or if they can't sustain a planet, let them abandon it unless their doctrine prevents them from abandoning their populations. It would be interesting to see the major factions be a bit more organic, and to see more of their worlds in the green ledger-wise.
Let major factions saturation bomb each-other. If they go for total-war on each other they should potentially wipe out planets. If they want to kill a world more "humanely" then let them set up a blockade with a massive fleet, or several fleets that stay in orbit around a hostile world keeping it's stability and accessibility at zero until the blockade is broken.
Adding Minor Factions
When the sector generates, have the generation algorithm look for systems with unusually high value averages for the planets present and mark them. As the game goes on, let those systems be populated by non-core factions with semi-randomized tech, doctrine, and hostility.
The small factions could replace the independents for the most part, or be a sub category of the independents. Their tech would be mostly trash, but with one or two blueprints for military ships at each hull-size (2-4 frigates, 1-3 destroyers, 1-2 cruisers, 0-1 capital ships). They would also have the basic weapon packages with a few extras at each weapon size.
From a game-play standpoint it gives the player either targets to fight with that aren't the core factions, or allies to work with if they've been more aggressive with the core worlds.
It also adds conflict to taking over the "best" systems in the sector, giving the player something to fight against in their colonization efforts.
Lore wise, it would make sense that the player fleet isn't the only one out there trying to rebuild humanity on the fringes, and not everyone building in the fringes is doing it for piracy reasons. Small factions are constantly cropping up and making trouble for the core worlds, and putting them all under the "independent" umbrella makes them feel like a unified faction instead of the minor factions they really are.
Lock Up The Good Stuff
Cobbling together a strong fleet feels pretty easy once you know the basics. Removing military grade ships from the civilian market, and adding extra d-mods to ships in the black market would go a long way to making the main factions feel more like dominant powers.
Removing proper military ships from the open market, most pirate fleets, most independent fleets, and reducing the options for the main factions would make them feel more distinct, and also much more powerful. It would also make finding "good" ships in salvage more exciting.
It would also make commissions with factions much more enticing, not only do you get a bounty for fighting their enemies, you also get to buy those juicy, exclusive, military ships from their markets.
Add Unique Industries
Factions should have powerful industrial or social practices that are difficult to use without a strong central government, very specific technology, or extreme loyalty from the populace. Things like a central bank for the TriTacs that adds a faction-wide boost to planet income, a military strategic center for the Hegemony that allows larger fleets, or a set of holy relic sites that improve stability on Luddic worlds.
Allying with a faction could give a player access to those bonuses, building up enough loyalty with a base commander might convince them to join you and bring their knowledge to one of your worlds (a unique skill on a manager?), rescued people from decivilized domain worlds may have knowledge about lost tech.
De-unify The Pirates and Independents
This has been in suggestions before, so brevity seems appropriate.
These people probably shouldn't even have a faction reputation statistic, and they certainly shouldn't be communicating as well as they do. Destroying pirate raiders, or a couple of smugglers really shouldn't be affecting the player's standing with every single other person who is decidedly not aligned to anyone.