Basically can you generalize adjunction to "graded adjunction?"
I have a hunch you would end up with something similar to some linear logic stuff. My thoughts are you can use monads for effect systems and you can use adjunctions for effect systems (call by push value is an example) and you can use graded monads for effect systems so you ought to be able to use "graded adjunctions" for effect systems. I feel if you generalize that much you would end up with some sort of linear logic stuff.