Yes this is possible using the Alerts and Notices section of the settings.
You can get to there via http://yourdomain.com/scp/settings.php?t=alerts(http://yourdomain.com/scp/settings.php?t=alerts)
In there you can choose to have department members and managers to receive notifications when a new ticket is created.
In your example you can have client2, staff 3 and staff 4 in a different department from client, staff 1 and staff 2.
I don't think you have understood, what I am asking is
Client in Dept A
Staff1 in Dept B
Staff2 in Dept C
Staff2 is also a Head of Dept B
Client issues a new ticket whose helptopic is Dept A and assigned to Staff1 of Dept B
An alert is sent to Client, Staff1 and the Boss of Client but the same doesn't sent an alert to Staff2 who is the head of Dept B where Staff1 belongs to. Neither can we set up a system where the same staff can have 2 departments as in our company 1 manager is a head of finance and IT as well.