Yes, timing matters. The Medicare supplement open enrollment period starts on the first day of the first month in which you’re age 65 or older and enrolled in Medicare Part B. In some states, you can buy a plan on the first day you’re enrolled in Medicare Part B, even if you’re not yet 65. If you meet certain criteria, such as applying during your Medicare supplement open enrollment period, or if you qualify for guaranteed issue, a company can’t use your medical history to determine your eligibility. Rules in some states may vary.