Pay for a letter from a lawyer, usually they increase the severance.
You would get silent applause by everyone who reads it, but not going to help severance package. If you want a settlement, you need a lawyer to demand it for you. Lawyer can add that part in as leverage. You will be let go with more than they were going to give you. Make sure you are asking enough to cover the price of the letter he sends.
t. dun it twice
A colleague did that as he was quitting. He copied upper level management on a rant full of disgust. He had a job lined up, though, and wasn't looking for severance.