Federal income tax applies to severance payments, as they are technically income. The amount withheld depends on your total income and the withholding allowances you claim on your W-4 form. Social Security and Medicare taxes also apply. The standard rates are 6.2% for Social Security and 1.45% for Medicare.
Tax Implications in the U.S.: The severance payment would be considered additional income and would attract a flat 22% withholding rate for federal tax, along with any applicable state taxes (depending on the state). Social Security and Medicare taxes would also be applicable, subject to wage limits.
Employers. Employers are required by law to withhold employment taxes from their employees. Employment taxes include federal income tax withholding and Social Security and Medicare Taxes.
All you can do is ask. They'll probably say no but you're bound by the companies severance policy/program but legally it's not a required benefit. BUT keep in mind the company wants you to sign that agreement at the end of the day so you could get more. You could try and use trigger words during your conversation.