The Medicare Open Enrollment period is designed for enrolling in or switching Medicare Advantage and Part D prescription drug plans, not Medigap policies. In most states, insurance companies can deny you a different Medigap policy and you won’t have guaranteed issue rights, unless you are either eligible to switch under a specific circumstance or you purchased your Medigap policy less than 6 months ago. This means that in many situations, insurance companies that agree to issue you a new policy may write pre-existing conditions, waiting periods, elimination periods, or probationary periods into the new policy. However, you should check the specific rules in your state because some states have annual open enrollment periods for Medigap and some states provide more opportunities for Medicare beneficiaries to have guaranteed issue rights to a new Medigap policy.