Is it possible to capture an existing enemy starbase so you can start acquiring the resources it controls without destroying it and building one yourself?
There is an Ideology in the Benevolent tree, "Enticing" (Prominence III):
For starbases, this seems to be a one-time event that happens when the ideology is selected.
You didn't ask about planets, but to avoid confusion: Planets can be turned without Enticing, but it takes a lot of time.
It took me dozens of turns after this screenshot before the planet finally converted to me. The long time is due to the Unwaivering trait of the Drengin.