Severance offer, what should I ask for? - 8 months and counting

The company sent a severance agreement with a release of claims, and I am unsure what to do. 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 last year, and it settled down once I kept a simple log of every call and form.

Read the release carefully. Mine included things I did not expect, like a non-compete.