During boom there are reports of tempoary upgrades, for now it is a mechaism via CG only that stations upgrade, but the community have been screaming, in 2.1 we got the retreat and invesment states and such things are in the 10 year plan.
Rumoured also are passanger colonists which over time will affect population growth of systems u deliver them to
So it is not yet implemented fully it may well in 2.2. 2.3 or onwards.
What I found so far.
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BGS -
Back
Ground
Simulation
Ways of affecting influence
Guide by the Alliance Elite Diplomatic Corps (AEDC)
States heavily depend on the manipulation of influence values. This can be achieved by all the activities in Elite Dangerous.
2.1 Missions
When accepting missions you might have wondered what the meaning of this influence (
low,
medium,
high) is. This comes to play in the
BGS. Missions are a good way for manipulating influence values and seeing some of the surounding systems. Doing missions is a must when a faction doesn’t have its own station yet.
2.2 Trading/Mining
As soon as your faction has its own station you can use other means of supporting them. You can use your trading ship and trade with the station of your faction. Selling them goods with a good profit results in an increase of influence. Important to note here is that rare goods don’t count towards the BGS.
Alternatively you can fly your mining ship to the nearest pristine metallic ring and mine for valuable ores and
minerals. Selling these (coupled with mining missions if possible) gives this faction also an increase in influence.
2.3 Bounty hunting
If your faction of choice is the ruling faction of a system, you can support them by “arresting” bad guys. Simply fly to location that is frequented by wanted ships and collect their bounty. Afterwards cash the bounty in at the nearest station controlled by the faction you want to support. Only bounty issued by your faction helps them gain influence. Cashing in other bounties might be advantageous for other factions.
2.4 Combat
When two factions are in a state of war or civil war, you can hop into their conflict zones and fight for one faction. Make sure to switch to this faction in your funtions tab. Cashing in combat bonds at the nearest station helps this faction in their war effort and might provide them with a new station.
2.5 Exploration
Even when scanning systems outside the bubble or simply honking undiscovered systems inside the bubble, you can still support your faction by selling your exploration data at their station. Be carefull not to sell too much at once since you might waste influence. Limit yourself to a maximum of 10 million
in exploration data per day and per faction.
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It's just that I can't find that everything written above means that the strengthening of a single faction and good relations with her, grow and rise quality of supplys and offers (markets, modules for fitting) in the station controlled by the faction.