I suppose you can do it in a couple of different ways. One, where the base moves around with you, where it's a character in the party in it's own right which changes as you adventure and develop extra features for it - which can be the case in games where a party has a spaceship and that ship matters, or when the party is part of a group that moves around and alters along with the players. Or it can be a fixed place that you keep returning to, and which your actions alter (something that is done rather well in a number of games outside the RPG sphere, Gloomhaven being a very good example which isn't really imitated in many RPGs).
Obvious examples of the first include games like Star Trek Adventures, that one Paizo AP with the pirate ship, or the Nomad Clan game I played in through a fair bit of lockdown, where things we did led to significant changes in what the clan could do and therefore to our abilities/ For the second, Keep on the Borderlands could be done that, way (and Gloomhaven would be an obvious model), the player kinght's manor(s) in Pendragon, and Deep Space Nine (for an alternative ST) where the changes are less in adding new things to the station and more altering the world around it and having that reflected in what happens in the base.
It'd be pretty to make sure that some adventures aren't about going somewhere away from "The Base" but revolve around things happening there. Things which you can't solve by waving a sword or firing a laser, whether it's unrequited love or a bad harvest or the ship needing repairs and having to limp along while you fix things. Make the base one of the characters and it'll have a relationship with the players (and not just the characters).
