Is there a way to add Category drop down with in an incident?

Is there a way to add Category drop down with in an incident?

Hope this makes sense. 

Most (99%) of our users use email to open tickets, so the 'Category' field is left blank. We are wanting to track our incidents based on Category, so when a Technician opens an incident to reply, they are having to edit the incident to fill in the Category field before they can close the ticket out. 
Though it is not a major issue, it would be nice if they were able to change the Category field with in the incident page without having to edit.

Is this possible?  

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