It is possible to use TB with different sets of accounts, address books ec.
Those sets need to be separated in th registry. When everybody is using TB from their own Windows user account that's the default, but I understand from your message that you want everybody to access their mail from one user account.
In order to do the latter, you'll need to use a command line parameter to specify the registry path you want to use.
It's a hidden feature, basically created for the use of beta testing, so you won't find it in the help file.
Use this: /Reg:Dad as command line parameter, either from a batch file or a shortlink on your desktop.
The basic instance of TB will run using the settings from the registry path:
HKEY_CURRENT_USER\Software\RIT\The Bat!
The /Reg:Dad instance will use
HKEY_CURRENT_USER\Software\RIT\The Bat!Dad
The link in the shortcut would look like this:
"C:\Program Files\The Bat!\thebat.exe"  /Reg:Dad

When you start TB for the first time with a new reg-parameter, it will ask you for the specifics where to store its message base and such. Take care to use a different mail directory for every parameter (so not the default), because otherwise they'd point to the same mail accounts.

Note that you may use the same registration key for all configured instances of The Bat!, but that your license doesn't allow for multiple instances running at the same time.