Determining how many of one user is logged-on to the network

In our network, we use a few Generic users, to give some staff that rapidly
change general access to our computers (the programs that they use on the
computers have their own credentialing system, and that has individual users
setup).

We're trying to determine, on any given day, exactly how many users are
logging in, or, are connected to the network at once, using the Generic
accounts.

Is there a way to easily do this? Our systems are either Win2KProw/SP4 or
WinXPProw/SP2 and our ADS is 2003.

Thanks!