@SarahGen-- I don't know why @MikeMason did, but I took them together a couple of times for back and neck pain.
It wasn't my intention to take both and you are right that meloxicam is stronger than ibuprofen. How it happened was that I hoped the ibuprofen would be enough for my pain so I took that first. But when I didn't get pain relief, I also took meloxicam some hours later.
Thankfully, I didn't have any bad side effects from the combination. But I didn't take very high doses of either and like I said, I only took them together for a couple of days.