I have always been taught no, for these reasons:
"Phenylbutazone (bute), flunixin meglumine (banamine) and firocoxib (previcox/equiox) are all non-steroidal anti-inflammatory drugs (NSAIDs). Firocoxib has been shown to have reduced toxic effects on the gastrointestinal tract and kidney relative to its older counterparts, however, by combining ANY two NSAIDs you are increasing the risk of related toxicity.
In the past week, two horse owners told me that they were giving their horses Bute and Previcox at the same time, without veterinary instruction. They had no idea that they were doing harm, as they did not realize that these drugs have the same mechanism of action, and real potential for toxicity when administered in combination."