Yes, you can. In most cases, it makes sense to keep both, as you will have access to a greater choice of doctors and other medical providers.
In some counties of New York State, you may be encouraged to join (or be passively enrolled in) a FIDA plan that delivers both Medicare and Medicaid services on an in network basis. FIDA stands for “Fully Integrated Duals Advantage,” referring to people who are eligible for both Medicare and Medicaid. As long as you have the right to keep traditional Medicare, you may want to seek advice before enrolling in a FIDA plan.
For effective planning, if you are making any transfers of your assets now, the five-year look back period must be taken into account.