Should I negotiate my severance? - 24 weeks in

I was offered 4 weeks of severance after 4 years as an insurance claims processor, and I have a few days to sign. This is my first time dealing with any of this. There is a non-disparagement clause. Did anyone negotiate and succeed?

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

An hour with an employment lawyer cost me a small fee and made me feel much safer about signing.