We do not have a "supplemental" plan but we do have my husband's insurance coverage from the company from which he retired. So that serves the same purpose. No matter what you call your additional medical coverage, it acts as a fill-in or gap coverage. Here in the US, once you reach that magical age when Medicare is available, you must sign up and use it for your medical costs. Depending on whether or not you are currently working (usually full time) and are covered with medical coverage through your employer, Medicare will be primary or secondary. If you have coverage where you work and are age qualified for Medicare, your employer's coverage is primary. If you are not employed or if your employer's insurance does not cover you and you are age qualified for Medicare, Medicare coverage is primary.
No matter what "supplemental" coverage you get for yourself, you should definitely make certain that you have prescription drug coverage - either in a supplemental medical plan or a stand-alone prescription plan.
We have been blessed with excellent coverage and are so thankful for it. I hope you are able to.