Could innies have their own innies? 

For example, a lower-level floor where they lose all memories of their innie life and continue to have no memories of their outie life, while only retaining the memories of what happens on that floor. And maybe even additional "nested" innies when they go to other floors/areas? 

I suppose this is really a two-part question, with the first being whether it’s technologically/physiologically possible in the world of Severance, and the second being whether this may actually be happening. 

With regard to the second part, it would be pretty hard (though not impossible) to pull this off without the person being aware of it happening, and the fact that nobody has spoken about it suggests that it’s not. And if it were possible, you would expect Lumon to make use of it, for example by invoking an “inner” innie when they visit other departments (since it’s established that Lumon doesn’t want them to know too much about what happens in other departments). 

Based on the above I’m thinking the evidence (somewhat) indicates that it’s not being done and that it’s not possible, but I’d be curious to hear others’ thoughts.