Instead of base items being purely cosmetic or utilitarian, we can have base items unlock new content.
This could be small content, such as:
Box of 12 Ghosts- Ghosts periodically escape and have to be put back in the box. Abandoning this box could have a moral aspect.
Pinball Machine- you play pinball on it :P
Prized Possession- It's stolen at various points by your Nemesis, and must be gotten back.
Onyx Cat- Some times comes to life and goes for a walk on the town.
Or it could be rather big
Aether Door- Unlocks access to Aether missions. Kind of other dimension based missions.
Alien Shuttle- Unlocks orbital missions. Upgrade with jump drive to unlock more missions in other solar systems. Upgrade with super jump drive to unlock missions in other galaxies.
Simulator- Allows you to play various challenges
Tachyon Telescope- Let's you detect time holes in open world.