From personal experience, I could not get this done, even though my doc was 1 of only 3 subspecialists in a county of 1.5 million.
I called. I sent faxes. I wrote letters. I sent e-mails. I threatened withdrawal from the network (and followed through). No one cared or would listen. I was told again and again "If you don't like our fee schedule, you can terminate your contract." I spent a year on it. We then hired a consultant who "specializes" in this and he couldn't get it done either.
I do STRONGLY recommend joining an IPA, which is a group of practices banding together. There is typically a fee to join and there are requirements (using EHR, demonstrating cost effectiveness, meeting certain screening metrics, etc.) Each IPA's requirements will be different. Since the IPA is a large group of physicians, they have negotiating power with the carriers. Some IPAs also offer additional benefits like discounts on medical or office supplies and may offer simple assistance with a legal question (like does this employee qualify for OT?). When we joined an IPA, the largest carrier (almost 40% of our patients) saw about a 30% increase in fee schedule. Medicare obviously did not change, and other carrier increases were 10-30%.
There are also ACOs but they typically have a much more structured model. You may have to use their specific EHR, may have to agree to send patients only to a specific hospital, etc.
I would look at what IPAs are available in your area and see which might be a good fit for you.