No, you generally should not take ibuprofen and meloxicam together unless a doctor has specifically told you to do so. Both are NSAID pain relievers and combining them increases the risk of serious side effects without giving better pain relief.
Why they should not be combined
Both ibuprofen and meloxicam irritate the stomach and intestines, so taking them together raises the chance of ulcers, stomach bleeding, and perforation. The combination also increases stress on the kidneys and can worsen blood pressure and cardiovascular risk.
What to do instead
For additional pain relief, doctors often recommend pairing meloxicam with a different class of medicine, such as acetaminophen, rather than another NSAID like ibuprofen, but this should still be confirmed with a clinician who knows your history. If your current dose of meloxicam is not controlling your pain, contact your prescriber before adding ibuprofen or changing doses on your own.