If I had my way, I'd probably alter individual star systems like this:
Increase the system size to 32x32x32
Arrange planets, dwarf planets, moons, etc. into one or two planes (32x32) around the central star.
Replace 1 or 2 mid-range planets with a ring of asteroid sectors. Do the same at the outer-most orbit on the plane.
Place random asteroids randomly within each 4x4x4 block off the middle plane where the planets are.
Keep the middle of the star system above and below the star clear, with a 4x4 corridor running vertically through the star.
Place a trade station both at the top (zenith) and bottom (nadir) of this corridor if the system contains more than six planets.
Place a trade station near any earth-like planets with a 50% chance. (If it is earthlike, it will have a 50% chance of being colonized, with a trade station.)
On Earth-like planets with a station, place at least one random city and/or techno-pyramid.
On Earth-like planets without a station, place random creatures with a 50% chance. (About half of the uninhabited planets are uninhabited because of hostile natives.) Also have a 5% chance to place a random city or pyramid.
On other planets, 5% chance to place a station.
If not a station, then a 5% chance of a random creature.
If not a random creature or station, 15% chance of a pirate station.
Galaxies would be changed like this:
Each galaxy is 16 times as big on a side.
While each system is twice as big, place it randomly in a 4x4 "system-sized" area. This will "knock" each system out of the regular grid pattern enough to look a little more natural. This will also introduce more void between star systems. Maybe have the option in settings to allow more than 1 system in a 4x4 "area", depending on how close to the center of the galaxy that 4x4 area lies.
With these changes, each galaxy will be much bigger and have approximately 8x as many systems, due to having double the number of systems on each of its three axes.
Correction: I like the idea of a galaxy being only one or two systems (or in my case, 4x system sized areas, to allow exactly one system on the plane, but to be off the axis a little. At twice the system capacity on each side of the grid, each galaxy would have room for 4x as many systems on the galactic plane.
Every galaxy should have one (or two in a binary co-orbit) black hole(s) right in the center, with fun stuff like trade stations arranged just outside the "event horizon". This should probably be a starting point for a natural singularity-warp-gate system that travels all around the galaxy. This central area could be a focal point for several types of future options, events, and galactic features.
At the outer edge of the galaxy, beyond the edge systems, line the empty sectors surrounding a galaxy with a heavy pirate/threat presence. That way, each galaxy becomes an enclosed eco-system, encouraging players to remain in the galaxy, but allowing them out if they really, really want to. One can "punch out" of the galaxy to reach void space (again, Schine was planning something "fun" for deep void space at one point.) And if not "punch out", then run the blockade and out-run the pirates out into deep space. That could be fun too. Heck, blockade-running might become a new game type for some players.