[AccessD] OTSH: TS + Access ADE problem

I have a special-purpose version of our app that will be run only through
Terminal Services. A windows user called X was created. A SQL user called X
was created. TS was configured to run this and only this app (i.e. quit =
terminate connection). 

My question: can multiple users log on as X? Reason I ask: in testing, for
the first user everything works as expected. For each subsequent (duplicate)
login, Access gives its "read-only" message and then does not run the
switchboard, instead it simply opens with the app's db window hidden. Which
to say the least sucks :-)

Is this because multiple users are logging in with the same identity? Or
perhaps because I've forgotten to do something at the TS or Windows level?

TIA,
Arthur