Extra functionality for Departments within Companies

We’d like to be able to create divisions/departments within a Company so that Managers of departments can see all the tickets that their team creates, but not company wide tickets.  We could group the Customers into companies and departments. 

For example, you might have an Widgets Inc. company as follows:
Erica leads Engineering for Widgets Inc. and has reports Adnan and Bob.
Hermione leads HR for Widgets Inc. and has reports Rita and Brian.
Briony is the CEO for Widgets Inc.

Erica and Adnan is allowed to see all tickets for Engineering but not all tickets for Widgets Inc.
Hermione is allowed to see all tickets for HR but not all tickets for Widgets Inc.
Briony is allowed to see all tickets for Widgets Inc. (including Engineering and HR).