Severance packages are frequently presented as a ‘take it or leave it’ proposition. In some cases, for example in a widespread layoff, this may be true, and there may be little room to request additional pay or changes in the other terms of the agreement.
Very often, however, there is room for negotiation even if it is presented as a final package. There are really two levels to this process. The first is between you and either management or human resources, if you are able to establish a dialogue about what you want. Sometimes this is more money; other times you may ask to be released from a non compete, or alter some other term of the agreement.
The second is a legal negotiation, in which you retain an attorney to articulate the legal claims you might have against the employer, and ask for additional compensation in exchange for a release of those claims. This should start with an assessment of your situation by an experienced employment lawyer, who can give you an idea about whether you have claims and what they may be worth, so that you can compare that to what is being offered.