I didn't really mean to do it. Honest.
I triggered the Benevolent Ideology perk, Enticing. All planets and starbases in my territory flipped to me. I was looking to get a few minor faction planets I had planted Culture starbases by in preparation for the flip. I had a total of 5 administrators left after doing all tech increases. It was tight. I expected to get some of those administrators back when I didn't need the culture bases anymore.
I had forgotten about the AI's annoying habit of littering my space with resource mines. I wasn't using those resources, they seemed to think, so why not? And every one of those mining bases flipped to me. I now have a list of about 40 resource mines and totally ridiculous amounts of resources. I destroyed a culture base just to test, and now I have 6 administrators.
There is a hover tip that says I am using 96/102 administrators. I am on an Immense map. I am pretty sure that is a higher max than I had before. My guess is you get the administrators along with the starbases. When I decommission two of the newly acquired starbases, my available administrator count goes up to 8 and the hover tip says 94/102.
Yay for being Benevolent!