Can I take methylprednisolone and aleve at the same time?

Only if your doctor thinks you should- I had a Pulmonologist who tried to out me on this combo, but I can't take prednisone due to bad side-effects.

Interactions between your selected drugs
Moderate
naproxen methylprednisolone
Applies to: Aleve (naproxen), methylprednisolone
Before using naproxen, tell your doctor if you also use methylPREDNISolone. Call the doctor if you have side effects such as unusual bleeding, severe abdominal pain, dizziness, lightheadedness, and the appearance of black, tarry stools. You should take the medications with food and tell your doctor if you have any of these symptoms. You may need a dose adjustment if you take both medications. This may be more likely to occur in older adults or those with a debilitating condition. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor.
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Other drugs and diseases that your selected drugs interact with
methylprednisolone interacts with more than 400 other drugs and more than 20 diseases.
Aleve (naproxen) interacts with more than 200 other drugs and 10 diseases.
Interactions between your selected drugs and food
Moderate
methylprednisolone food
Applies to: methylprednisolone
Grapefruit juice may increase the blood levels and effects of certain medications such as methylPREDNISolone. You may want to limit your consumption of grapefruit and grapefruit juice during treatment with methylPREDNISolone. However, if you have been regularly consuming grapefruit or grapefruit juice with methylPREDNISolone, do not alter the amounts of these products in your diet without first talking to your doctor or other healthcare professional. Contact your doctor if your condition changes or you experience increased side effects. Orange juice is not expected to interact.
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Therapeutic duplication warnings
No therapeutic duplications were found for your selected drugs.

https://www.drugs.com/interactions-check.php?drug_list=1607-0,1690-2475