No — ibuprofen and naproxen (Aleve) are both NSAIDs and should not be taken at the same time, because doubling up raises the risk of serious side effects like stomach ulcers and GI bleeding; if one isn't enough, ask a pharmacist before adding anything.
Ibuprofen and naproxen belong to the same drug class, non-steroidal anti-inflammatory drugs (NSAIDs), and work the same way (blocking COX enzymes / prostaglandins), so taking them together gives no extra benefit but stacks the same harms. The NHS states plainly: "Do not take ibuprofen at the same time as other NSAIDs, such as naproxen or aspirin," because it "can increase the risk of serious side effects like stomach ulcers," and gives the matching warning on its naproxen page ("Do not take naproxen with ibuprofen or other NSAIDs"). MedlinePlus likewise warns not to take nonprescription naproxen with other NSAIDs such as ibuprofen, and notes NSAIDs can cause ulcers, bleeding, or holes in the esophagus, stomach, or intestine — risks that can occur without warning and may be fatal.
Pick one NSAID, not both, and stay within its label dose; do not run them together to "boost" pain relief. If a single NSAID isn't controlling your pain, the NHS says it is generally OK to add acetaminophen (paracetamol) — or to alternate timing under a clinician's guidance — and to ask a pharmacist or doctor before combining any painkillers. Higher risk of NSAID-related GI bleeding applies to people over ~60, those with a history of ulcers, and anyone also taking aspirin, blood thinners, oral steroids, or SSRIs/SNRIs — they should be especially careful and check with a professional. Stop and seek urgent medical care for signs of GI bleeding: black or tarry stools, vomiting blood or material that looks like coffee grounds, or severe/persistent stomach pain. Only take two NSAIDs together if a doctor has specifically prescribed that combination and told you to.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.