K2 Worklists for teams

Yes, your requirements sounds like it matches the default behaviour of K2.  In your workflow you would typically assign your activities destination users to a K2 Role, or AD Group .  The default behaviour creates 1 slot for that activity which means it can be assigned to multiple people but only 1 person can perform the task.

How it works is when a user checks their K2 worklist it'll show any K2 tasks (worklist items)  assigned to roles or groups that they are part and assigned directly to them.  The task's status in the K2 worklist shows as being Available.  If the user clicks on one of the tasks assigned to a role or group it'll open up the associated form and occupy the 1 slot for that activity.  This basically means they now own that task and that specific tasks now disappears from the other group members K2 worklist.  The task's status in the k2 worklist will change from available to open.

As I mentioned this is the default behaviour and can be changed to suit different scenarios.  It might also be helpful to review the following whitepaper which goes into more details about the different destination rule options and what they mean:  http://help.k2.com/en/AdvancedDestinations_Whitepaper.aspx 

I may not understand exactly what you're asking. 

However, the k2 worklist does allow filtering and grouping which might provide the differentiation that you are asking about.  In SharePoint you can also add multiple K2 Worklist webparts to the same page and set up filters and grouping on different process names and/or different columns the worklist provides like Activity.

The process designer could also use the process folio field or the activity names themselves which show up on the K2 worklist to provide a clear indication which are team tasks vs personal tasks.  Then the filtering/grouping/sorting provided with the K2 worklist can help the user prioritize.

Tim