You should be able to assign an approval task to a team rather than have to select individual people. This means that it is constantly having to be managed and updated to remove and add people that move between teams.
You should be able to assign a task or service request to an agent group rather than to specific people.
ATM it looks like you can only send an approval email, you should be able to just forward the service request or a task with the approval and reject option and be able to change the status or an approve or reject option appears for that stage for that team to approve or reject.

