Other than Medicaid, could I really cancel it out to get private insurance?

Okay so I get child disability (a bit over $700 a month, close to $800) and in my state that qualified me for medicare and medicaid to cover the medicare costs. However, since I'm also getting lots of backpay from SSA and saving a handful of it for housing later, I know that if I keep over a certain amount for roughly 6 more months I could lose medicaid but i was wondering if I really had the option to use a private insurance to cover medicare instead of medicaid? What are the pros and cons? Without medicaid, over $200 is taken out of my check per month, would using private insurance help the issue too?