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.

https://www.cms.gov/Medicare/Eligibility-and-Enrollment/Medicare-and-the-Marketplace/Downloads/Medicare-Marketplace_Master_FAQ_4-28-16_v2.pdf