You can. Most big companies have a standard severance package formula, language, non compete contract you sign.
Trying to negotiate a severance would be a sign that you do not trust the company (or believe that the company is stable), and could lead to your offer being rescinded.
During negotiations, emphasize your contributions to the company. Highlight your achievements, skills, and the value you brought to your role. Demonstrating your positive impact can strengthen your position and make a case for more favorable severance terms.
Some factors that are often considered include length of employment at the company, your position or rank within the organization, salary, and individual circumstances relating to termination. Some employers adhere to a written contract or employment agreement or policy that was outlined previously.
Neither the California Labor Code nor the federal Fair Labor Standards Act require employers to offer severance agreements to departing employees. Instead, severance agreements are provided by employers to accomplish a specific goal.