You can use plain get and put to interact with the outer state, and you have to apply lift to use the inner state. This problem, which for almost any other combination of transformers is solved by mtl's web of MonadState instances, is an example of why the topic of "extensible effects" is so hot. You are basically asking to add, and later subtract, a new state "effect". Barring rewriting your original state type as a product that includes the new one, there isn't really a neat way of doing this.
I'm not sure what happens if I apply a StateT to an existing State or StateT monad. Not sure how 'get' and 'put' would function, or if I would need to lift get and put to choose which state to access.
D
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