There are at least 3 types of supplemental coverage - std 'medigap' (types F, G, K, etc.), Medicare Advantage, and employer-provided coverage. My former employer-provided coverage, for example, is pretty lousy WRT co-payments until I hit the max out of pocket, and it's not great on meds, but it covers many doctors who opt out of Medicare, and it covers a number of items that Medicare doesn't cover (it paid for hearing aids a few months ago, for example).
You need to check with HR to get details, because employers have wide latitude. Also, make sure the coverage is 'creditable', which means you won't be penalized if you want to switch to advantage or a combo of medigap and part D in the future. (The people who forced Part D into being didn't make it mandatory, but IIRC if you ever want it and don't start when you're 65, you'll have to pay an extra 1% for every month that you delayed enrolling.
Also, remember that Medicare stars at 65. You lose some SS benefit unless you wait until you hit 'Full Retirement Age', which appears to be 66 for people born between 1943 and 1954.