Medicare advantage plan are run by private companies and approved by CMS. Usually employer provide these plan for more coverage than Medicare. In this scenrio all your claims covered by Medicare advantage plan. Medicare and Medigap will not pay your claims.
The only problem in the Medicare advantage plan is patient has to see the PCP before see other doctors. In other words referral will be integeral part here

List of Medicare advantage health plans.

Medicare Health Maintenance Organization (HMOs)Preferred Provider

Organizations (PPO) Private Fee-for-Service Plans

Examples

Advantra FreedomAarp MedicareEvercareHumanachoiceSecure horizonCigna MedicareTodays option
Most of the plan covers patients drug prescription also.

More resources
https://whatismedicalinsurancebilling.org/2009/08/medicare-plan-or-part-d.html
https://whatismedicalinsurancebilling.org/2008/08/medical-billing-concept-hmo-and-ppo.html