You can take my game… when you pry my cold, dead fingers off the board!
Since they are written assuming just 1 starbase, the rules don't exactly make it clear if you get an extra die for each starbase in battle or just roll 1 extra dice if you have at least one starbase. I suppose I would go with each starbase myself though (which seems the consensus)... assuming multiple are allowed.
"Starbases provide support for your Ships in Space Battels. When you have Ships in Orbit of a System you Control with a Starbase, roll an additional die to Hit."
(And blast the rules pdf again for not being searchable and not being able to copy/paste!)