It seems (ha!) possible to design the logic for such a system with deniability, like the system has to use the second/third/fourth password to attempt decryption before you know if the padding is encrypted or random noise [if the specific encryption has a signature then each install could encrypt the empty space with a few keys taken from urandom].

First password accesses clean files, second one accesses dummy [legal!] fetish porn collection ... do border guards hold you to get a third password?

An analogue analogue might be: I have a book full of "random alphanum text", I have two (or more) one-time pads for decryption of portions of the book, I also know the page/line the actual cyphertext starts at. The rest of the text in the book is random quotations encrypted using a selection of further random one-time pads. Can forensics find that there is a "hidden" n+1 plaintext when I give them the n pads and starting points? Seems impossible??