As I remember you need to a specific alpha tech. You can build a new megastructure on your starbases to upgrade them. Beware that the process consumes the constructor used to build it.

Ah, no wonder I never figured it out. I never get that far before everything dies.

Its not an alpha tech, its the precursor star base. You get it the same way to get the new ships from the reimagine, eh, "guided quest". Very recourse intensive to unlock, basically have to do extreme allocation every time, but you get some extremely powerful modules (like a single one that gives 5 shipyards) and some truly disgusting defensive numbers. good fun for when the upstart next door gets cranky and you show them your printer station churning out battle cruisers and escorts like they where corvettes :)