Yes that would be fine, but you may want to just take more of the codeine. Just look at the prescription, these drugs usually come with 325 or 500 mg of acetaminophen, or the second number (ex, 5/500...
Anti-Inflamatories such as Ibuprofen are not contra-indicated based on taking codeine. You would also be able to take Paracetamol (unless your codeine is in co-codamol). I would advise against taking...