How long could I take the max dose of Aleve (naproxen) for maximal anti-inflammatory effectiveness. 1100mg per day, OTC 3 tabs q12hs?

Several weeks. You don't need the max dose to get the max effect. If used to relieve symptoms of arthritis 2 tab bid time contingent or around the clock. You also get the analgesic benefit for mild to moderate pain. Take in consideration that you may experience serious side effects during treatment with this medicine. Make sure that your doctor check your progress at regular visits.