What if all servers would hold some random bits and no one would have any whole file (only the clients would be getting whole files)
https://en.wikipedia.org/wiki/OFFSystem
Basically people would be hosting random-looking blocks of data, but users could be instructed to XOR two carefully chosen blocks together, producing a meaningful file.
Because of the nature of XOR, if Alice sees that Bob is hosting a file F, she could generate and host a file G, such that F XOR G produces a banned file, providing plausible deniability for Bob (as long as he can point to a file H such that F XOR H produces an innocent file).