Severance offer, what should I ask for? (Providence)

My manager said the package is final, but the letter gives me time to review. This is my first time dealing with any of this. It includes health coverage for a couple of months. Did anyone negotiate and succeed?

Thanks for writing this out. I went through something close to it 8 months ago, and it got easier once I kept a simple log of every call and form.

I asked for two more weeks and a neutral reference. They agreed to the reference and added a week.