You can put a D-tuner on one (if you can find one and if the machines aren't too close together).
And, of course, you can tinker around with running pickups to separate amps (via pedals).
If it's an older one you can see if the vintage/modern pot is an option to tinker.
You can replace the treble pickup (I have an SD on one, with series/parallel & single coil switches).
You can replace the neck pickup (but I wouldn't).
Bartolini do a supplementary pickup which goes in the string mute cavity. (I've sometimes wondered about putting an E-Bow or Gizmo type thing in there!)
Some people add more pickups, including a "humpbacker" to fit between the treble pickup and the bridge.
You can replace the bridge.
You can change the pickguard/scratchplate.
You can split the pickguard/scratchplate to allow access to the controls without having to take the whole thing off (like a 4003(?)).
You can put a surround inside the treble pickup mount to close off the surrounding hole after you've taken off the cover (which you must do, unless you have one with the horseshoe magnets). The slot-in items there usually have a thumb rest.
You can add a thumb rest across the top edge of the pickguard.
You can add shielding to the body cavities.
You can replace the strap buttons with schaller-compatible straplocks.
If you like soldering irons you can modify the output jacks to 2 x mono instead of mono/stereo.
Apart from that, there's not much you can tinker with...