How many starbases can you fit around a planet? A group of planets? I could not wrap my head around that math problem, so I scripted up a simulator. Over many trials, the simulator's best result was 5 starbases around a planet with the default range, 8 starbases with the first range upgrade, and 12 starbases with the second range upgrade. I don't know if these are the theoretical maximums, but I was able to get 'er done with 12 starbases, turning Earth into a super planet post approval and production nerf (i.e. Beta 3).

It was super expensive. 12 starbases all with all the manufacturing and approval upgrades, and most with one or two range upgrades. I could have done better with adjacency bonuses, but I was kinda hosed with the capital placement.

The script works to maximize coverage of multiple worlds, though it does not currently take into account the edge of the galaxy or other obstructions. For example it was able to find a solution of 8 coverage (4 on Earth, 4 on Mars) using 5 starbases in this game's solar system, which was almost a worst-case scenario.