Yes, you can alternate between Tylenol (acetaminophen) and Aleve (naproxen) every 6-8 hours. Note: The maximum daily dosage of acetaminophen is 4,000 mg. The maximum dose of … naproxen is 1,500 mg (equivalent to 1,650 mg of naproxen sodium) per day.hose with liver damage should not take acetaminophen, and anyone with a history of stomach bleeding, or that has a risk of stomach bleeding, should not take NSAID drugs, including Aleve or Advil. NOTE: I am not a doctor or a pharmacist.