Two NSAIDs generally are not recommended to be administered to the same dog at the same time.
As a result, when it is necessary to switch a dog from one NSAID medication to another, oftentimes a “wash out” period is necessary. The “wash out” period allows the dog’s body to clear the previous drug from its tissues before the new NSAID is administered. This “wash out” period helps reduce the potential for adverse effects from the medications.
Full article Pet Health Care Gazette: Switching Your Dog Safely from One NSAID Medication to Another