Does anyone know what the major companies offering health care in the U.S. are; do they allow you to have?

medi- cal as well as their health insurance , because doctors say that medi - cal is not good enough and you need better health insurance, so if you want to buy your own health insurance and have medi- cal , does anyone know if any company will allow an individual to have a policy as well as have medi - cal so that they can be seen by a doctor who wants the patient to have good insurance ?