Can Workflow Tasks show BOTH Individuals assigned AND Groups?

I have a workflow on a SP 2013 list that uses flexi-tasks, and of course has an associated Workflow Tasks list.  When an item is assigned to someone via flexi-task, the assignment (item) in the Workflow Tasks shows the name of the INDIVIDUAL to whom it's assigned.  Sometimes it shows the name of the GROUP to whom it's assigned.  


If I were to create a new (choice) column in the Workflow Tasks list, is there a way to use this column to show where we are in the workflow, or the state it's in, in addition to the item showing the individual to whom it's assigned?

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