Although technically possible, it's like asking if you could build your own bridge across a large river.
Given the time, knowledge, and resources, you very well could negotiate your own debt management plan.
But, if you want to save time, frustration, and money, it's best to let seasoned professionals do the work for you.
Remember, a successful credit counseling service such as Credit Advisors Foundation has years of experience and contacts in the field, working with creditors on a first name basis.
Some creditors actually finance a portion of the administrative costs of a debt management plan and provide the best concessions through such a program, so in many ways it does not make financial sense to negotiate it for yourself.