1. What you have is a situation called "Secondary Payer". Supplement normally refers to a Medigap plan.
2. You cannot be sold a Medigap if you have a Part C Advantage insurer.
3. Whether your Advantage plan pays first on a claim, or your group plan does, depends on your Advantage plans rules, and the number of employee's in the group plan.
4. The Medicare website has info on Secondary Payer if "Original" Medicare + a group plan is involved, but no info if Original Medicare is replaced by an Advantage plan.
5. See
https://www.medicare.gov/supplements...ther-insurance for some background info.
6. You should call your Advantage plan and ask them how they deal with a Secondary Payer.
Also this article may also help understand the issues:
https://www.planprescriber.com/medic...condary-payer/