With piss and vinegar and a sincere belief that you deserve better, but with the clear understanding that you’ll likely get nothing.
So set your sights on something realistic and smaller.
I got them to sell me my work laptop for well below its depreciated value (14” M1 MacBook Pro kitted out with memory and storage for $800) which is what I went in hoping for. I had some real strong arguments for more severance which were all expectedly shot down, so when I asked for a discount on the laptop, I got it and I won.
In my case I knew the worst that would happen is they say no. That’s not gonna be true everywhere so there can definitely be some risk of losing the severance all together by asking for more, but if you have a good relationship with management and know they’ll come to the table in good faith it’s worth the time. If nothing else you come to the table and let them know you understand what the severance is all about (the non disparagement clause is all they really care about) and sometimes that’s enough to get them to give you something more.