One way to do this is to go into the Manage tab and add volunteers using an email address designated for that group. Then when you receive the list of volunteers for that group, you can go back into manage and make the changes
A second option is to stagger signups over time. For example, suppose you have three groups: A, B, and C with C being your general pool of volunteers. You can open up the event early for group A first with a password that only group A knows about. When it’s group B’s turn, you can change the password to one that only group B knows about. Then when it’s time for group C (the general pool) you can remove the password requirement. Additionally you can change the number of available slots each time to keep one group from grabbing too many slots.
A third option is to create different events for each group of volunteers that you can either password protect or simply make hidden. Then send each group the link to their signup sheet. Additionally you can designate someone in each of the groups to be an Event Administrator. This way the group can be responsible for signing up everyone in their group.