Have you tried to explicitly specify different directories for each user on the command line for Eudora? Basically on the "target" for the shortcut would have something like:

C:\EUDORA\EUDORA.EXE mboxdir

where "mboxdir" is different for each shortcut for each user. This will allow you to have different E-mail profiles for each user and keep the mailboxes separate. The "personalities" feature is used to specify E-mail logins on different servers from which you want to retrieve E-mail.

Probably the cleanest way however is to configure separate logins on the computer for each user, then set up separate desktop configurations for each login.