You must first be enrolled in Medicare before you are eligible for a Medicare supplement insurance plan, sometimes called Medigap. You are eligible to buy Medigap coverage during a six-month Medigap open enrollment period. If you wait until the open enrollment period passes, it may cost more to buy a Medicare supplement insurance plan in the future, or you could be denied based on current or past health issues. You are not able to purchase both a Medigap and a Medicare Advantage (Part C) plan.