Should I negotiate my severance? (Raleigh)

The company sent a severance agreement with a release of claims, and I am unsure what to do. I have read a lot of threads here and could not find my exact situation. I do not want to leave money on the table. Did anyone negotiate and succeed?

Thanks for writing this out. I went through something close to it 10 months ago, and it settled down once I kept a simple log of every call and form.