Your severance offer is highly negotiable. How you approach the company to request additional severance is what makes all of the difference.
In most instances the best way to negotiate for more severance is to send a written request in a verifiable manner (i.e., an email or letter by FedEx) to the company. The First Step: identify the target. The target is a senior executive who has the power, and either or both the inclination and motivation to improve your offer. Human Resources or legal are almost never the proper target. The Second Step: prepare the letter. The tone of the letter should be respectful. In addition, the letter should specifically set forth your reasonable proposal as to what additional money and benefits would make your severance fair. The Third Step: support your request for additional severance with rational arguments based on your unique factual circumstances.
It is your unique situation that will ultimately dictate the improvements, if any, the company will make to its initial severance offer. As such, avoid, unless truly relevant, referencing what you have “heard” others have received. First, it is rare that what you “heard” someone got turns out to be accurate. Second, most employers are turned off by a request that is based on what you heard others got. Also avoid threatening the company with lawyers, lawsuits and publicity. The company has lawyers too, is in a far better position to drag out a resolution and there is truly no such thing as bad publicity if you could even interest anyone in your story.