I've learned a decent amount about the coding, and I thought I'd share my discoveries.
Working Systems
Currently, I've got Weapons, Drones, Shields, and Cloaking working. These systems can be theoretically upgraded to infinity (untested but theoretically supported), since they use predictable formulae fhe game can use to calculate an endless steam of upgrades.
Weapons and Drones use the same formula: 1 upgrade = 1 max power. Of course, the eventual practical limit is based on weapon slots and weapon power requirements, but you can push these to the next galaxy if you want.
Shields uses the formula of: 2 power = 1 shield layer. I've gotten this working up to 8 layers of shielding (which, btw, can block missiles

Cloaking uses the formula of: 1 power = 5 seconds of cloak. And yes, this goes infinitely; with cloaking 12 you get a minute of alone time.
Broken Systems
Some systems cannot work with higher upgrades, because their upgrades are not formulaic.
Currently, I've only tested hacking, which freaks out past level 3 (at level 4, 0 seconds of hack time, at level 5, -2.14 BILLION second hack).
Untested Systems
These are systems I haven't tested: Engines, Clonebay, Medbay, Oxygen, Mind Control, Artillery, Teleporter.
I have reason to believe that Teleporter and Artillery might be able to have 1 more level squeezed out of them (due to their effects eventually reaching 0), Oxygen and Medbay should work, Clonebay probably won't (due to jump heal), and I'm pretty sure I've read somewhere that Engines just don't.