Generally, no. It's illegal to sell you a marketplace policy if you have Medicare. Section 1882(d) of the Social Security Act makes it illegal to knowingly sell duplicate coverage to a Medicare beneficiary.

If you already have a marketplace policy before you sign up for Medicare, then you can keep your marketplace policy. However, any tax credits you were receiving will end when your Medicare Part A coverage begins. That means you'll have to pay the full price for your marketplace plan.