Have you thought about the use of Queues? Sometimes a feature within a software package is so unique that it hints of being a major deal to implement. This means more training, change (everyone's favorite subject) and risk. Yes, change does bring risk.
Still Queues (despite the descriptive and yet fancy name) are a powerful feature that is not necessarily that hard to get your head around.
You can define a Queue in Settings, Business Administration, Queue. You give it a name, an e-mail address and assign it to a Business Unit.
You can add things to a Queue by assigning an Activity or sending an e-mail to the e-mail address you setup when you created the Queue.
How do you get things out of the Queue?
You open the Queue via Service, Queues, Select the Queue.
You then grab an item you want to work on by picking an item from the list and pressing the ACCEPT button.
Did I loose you yet?
Queues have three sections. The main bucket of things to do, the In Progress Bucket and the Assigned Bucket.
If you are not using Queue's but you really have activities that can be assigned to a line as opposed to always the same person perhaps it is worth reading up on them a bit more. The above pretty much sums up the basics.