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In World 11 (Miracle Tower), complex numbers of keys are introduced, but I wonder if in some sequel or spinoff, it might be fun to explore the properties of extending integer keys in other ways. Like instead of i, we could have a key that multiplies the count by ε (maybe named a "differential key"), where ε^2 = 0. Then I wonder if it would spice up puzzles since we can order them; in the sense that "1 key is greater than any amount of ε keys," so having 1 key opens an ε-door and just reduces your key count to 1-ε.

Interested to hear other mathematical extensions too though!! Really big fan of how far this game takes the concept of opening doors with keys. But I get it if this idea is TOO mathy.

A less mathy idea for some extension world:

In a new chapter, you find that star keys are "exact single keys of the star effect", and unstar keys are exact-zero of them. Every star effect you have gives you the amount of keys that you just used to open the door, and you can now have multiple, negative, and complex star effects! Example: having 2 star effects gives you the costs of doors when you open them; having -1 star effect makes you lose them twice as fast.

Together with this is introduced the Star Door/Lock, which requires the amount of star effects to open. You can still shred the door with a master key, and combo locks spend keys with precedence over star effects.

I had an idea for my fangame of IWL for Delta numbers and keys, where the Delta number squares to the amount of Delta keys you have.