ah I see, so like donations and doing missions and trades in your system?
Yep, that's it.
I've not really been experienced much with BGS and influencing states etc - any recommendations on guides to use etc?
Tricky one, that.
The only current general purpose BGS guide I'm aware of - and it's mostly right, and aiming to stay current - is
https://forums.frontier.co.uk/threads/bgs-guide-2024-2-0-released.629028/
(other guides you might find are almost all over five years out of date, and weren't exactly great accuracy in places even then)
But ... that guide, and indeed most other stuff you'll find, is written by and for people who generally want to put their faction in control of as many systems as possible.
This is a somewhat different situation: you want to put positive states on as many factions as possible, but it really doesn't matter who controls the system. So the emphasis on what you need to do is different.
Broadly speaking:
- complete missions (you might want to avoid missions which send you to your own system's Odyssey bases to do something unpleasant to them, though)
- trade in-demand trade goods to the ports you've built (they may need to come from out of system)
- if you have universal cartographics, sell there
- do some bounty hunting (use a KWS to get a wider set of bounties)
In general this is going to benefit your controlling faction more than the others, so you might want to compensate by running more missions for the others (as they're the easiest thing to pick who you work for)