I am looking for a pop client that allows me to log on from either of
two machines on my LAN and see the same address book, same inbox, same
outbox, etc.  Can't with Eudora, Thunderbird, or other well-known
clients.  I think can with Outlook but would prefer non-MS product. 
This is NOT two personalities on one machine, but one personality on
two machines.

You may be able to do it without actually using anything other than
default software. For instance if you can use Thunderbird but set up
one machine with a shared drive where you store the address book,
stored folders etc. Then permantently connect the other machine to the
shared drive and use the same preference files, stored date, address
book tht is located on the remote machine.

This way you get to use a well known piece of software but have access
to the information from both machines. It is also pretty much
Operating system independent as you can set up a network drive on
pretty much any operating system.

I hope this helps.

I support an office using a Eudora installation where the Eudora files
are on the server and a user can log on from any computer and get
their email.  This can also be done with Outlook by locating the .pst
file on the server.  The caveat is that you can't open it on more than
one computer at a time.

I've not worked with Thunderbird much, but I'd be surprised if you
couldn't do it with it.

You don't need to have a server to do this.  You just need to host the
files on one of your workstations.  I would recommend mapping the
drive as the same letter on both computers so you can avoid confusion.
 (i.e. create a directory on computer A named 'Mail' and map it as M
on both A and B.  Set up the program on both computers so that the
data is accessed from the M drive.)

Thanks for your suggestions.  I tried Vlad's idea already, with
Eudora.  I'm not sure why this happened, but the eudora.ini file got
corrupted causing the loss of messages in the two open mailboxes on
the host machine.  Perhaps this problem could be avoided if Eudora is
not running simultaneously on both systems?