Comment Speaking from experience, (Score 1) 98
it can be done. The key is to make sure your applications are opening the databases and recordsets in the proper share/locking mode, minimize the amount of time lock is in place, minimize the amount of time recordsets are open, and handle the runtime errors correctly.
Multiple users should be able to have read access to same database simultaneous, and still be able to update the database but at the same time.
First make sure all your network shares are setup properly for this, and you probably have a big enough user base to justify moving to a true client-server based database.
But don't listen to those who tell you to stop using Access just because it's not a "real" database system.