I won't say it can't be done, but here was my experience.
Over the years, I have tried to negotiate our fee schedule with almost every carrier, on multiple occasions. Unfortunately, I was successful only twice, and for very small carriers.
Basically, if you are a small private practice and represent only 1 or even a handful of providers, the insurance company just did not seem willing to bother. Their attitude was "Here is our fee schedule. If you don't like it, don't be participating." If you are a private practice, my recommendation would be to join a strong IPA or PHO in your area. The IPA/PHO has negotiating power and the insurance companies are more likely to listen when the IPA/PHO threatens to withdraw hundreds or thousands of providers if they can't get a better fee schedule. That is exactly the same situation for large healthcare organizations.
I thought as a subspecialist with only 3 doctors of the specialty in a county of almost 1.5 million people, I could get someone to listen. I was mistaken. I tried a couple of different types of proposals - across the board percentage increase over standard, payment as a percent of our billed amount, payment as a percent of Medicare, or even a carve out schedule where at least our most common codes could get better reimbursement. The 2 times I was successful one was for payment as a percent of our billed amount, and the other was to pay a flat additional fee for certain services. We did try using a consulting firm specifically regarding our in office surgical suite. Honestly, they seemed a little suspicious to me, and even their shady practices did not result in any additional reimbursement. As a result, we decided to withdraw from the 5 lowest paying carriers. The best business decision for us at that time was to join an IPA, which meant a 30-40% increase for our largest commercial carrier, and we would remain an independent private practice.
Eventually, we were incorporated into a large healthcare system which is becoming the norm in my area. The healthcare system has a significantly increased fee schedule for all carriers. When I saw what the insurances are willing to pay when you have negotiating power, it made me very frustrated that no one would listen when I wanted even a small increase.