Continuing our earlier work on write-efficient memories (WEM), we intr
oduce new models, where several persons use the same storage device. A
t any time instant, exactly one Of a prescribed set of users has acces
s to the memory, but there is no protocol which determines the moving
order. Among the constraints we analyze, the most interesting one is a
complete privacy protection. While a user stores new data, he has to
guarantee that those of the others do not get distorted. This leads to
fascinating new coding problems. We provide several code construction
s, as well as abstract performance bounds.