Should I negotiate my severance? - 7 months and counting

I was offered 12 weeks of severance after 12 years as an IT help-desk technician, and I have a few days to sign. This is my first time dealing with any of this. 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 7 months ago, and it got easier once I kept a simple log of every call and form.