Tenants Evicted with unpaid rent of 2 months

So tenants have been evicted. I have the judgement for the last FTPR which proves unpaid rent of 2 months. 

The question is, can i start the process of garnishment using that judgement and on a side i file for a large claim which would not include the 2 months unpaid rent but other costs/damages as they have been evicted before the lease expiration and did not finish the entire term.

What would be the best way to go about it.