I would really like to see something like the culture system of sins of a solar empire, minus the taking over a system with culture only.
it could be a system where the rate of spread depends on the distance, and there is a constant inwards spread, so say that coming from your home system, outward spread is 10, while inward spread for the game is 2, it would spread out at a rate of 8, as it spreads further and further from populated systems, it gets weaker and weaker, untill outward spread is equal to inward spread and it just stops, this way you have unclaimed space, can push back the boarders of NPRs just by having ships nearby, but they can do the same, of course there would have to be a way to determine distance between systems, and each system would have to reach a certain amount of border strength before it starts spreading from there, like an overflowing bucket.
This allows for border disputes and that ships near your border will make you want to take action, as they will be pushing your border back and other cool things like that. I just dont know what kind of limitations going outside your border would have, maybe unable to colonize, or a constant increase in the unrest of populated planets the further away from your borders it is