What we did was create different notification groups for each team but also chose other groups to display to each person.
For example we have the notification group "Network Team" and each network monitor alerts to that group.
But also we wanted the network guys to check the status of the servers, even if they won't receive any notification, so each user of the network team has both the "Network" and "Servers" group, but only the "Network Team" notification group.
That way we all have full visibility but alerts are sent only to those that need to be notified.
Hope that helps.