Very well put. And yes I assumed using the same key. the way I like to think about it is that if two completely independent schemes didn't maintain their random

Very well put. And yes I assumed using the same key. the way I like to think about it is that if two completely independent schemes didn't maintain their randomness when combined OTP would be broken and of course that's not the case (not the most accurate way to put it, I know). However I'm always cautious to just say "yes you can add layers" because the last thing I'd want is someone to then try and develop some hybrid scheme by just slapping stuff together that ends up being vulnerable because of key reuse or some other oversight.