If you're someone who rarely calls in sick or takes personal days and you have a good relationship with your boss, you can leverage that, too.
"Ask them to throw in a couple of weeks of pay based on the employee that you were," Thanasoulis-Cerrachio said.
Just be sure to get any changes to your severance agreement in writing, or all your smooth-talking could be for naught.
Asking for several extra paychecks or an extension of your paid health insurance or retirement benefits isn't your only option. In fact, unless you're at the top tier of management, asking for non-cash items could get you further.
If you're a telecommuter, "sometimes you can negotiate a full office -- the chair, the desk, the fax machine, the laptop," said executive coach Rich Gee from Stamford, Conn.
If the laptop's a few years old, there's a decent chance a larger company won't want it back, Gee said. Besides, he said, "companies don't want to be in the moving business" -- they just want an easy resolution to a messy situation.
Another suggestion from Gee: If you've been offered several months of subsidized health insurance but don't need it because you're on a spouse's or domestic partner's plan, you've just found another bargaining chip. Offer to trade the free health insurance for the free office equipment (or whatever else you'd like).
Not at the top of the career food chain? Not to worry. There are still some things you can negotiate.
"If the company provides outplacement services for X number of weeks, increasing that by two to three weeks may not make a major difference in their processes but may be a huge benefit for you," said Darcy Eikenberg, a career coach in Atlanta.
You can also ask for extended access to company office equipment (computer and printer in a communal office area, copiers in a reception area) to help with your job search, she said.
Consider asking for a recommendation letter on your way out, too, said Jeffrey Gordon, a professional contract negotiator from Raleigh, N.C. If your company has a policy that prohibits employees from giving recommendations in writing (some do), ask what they will say about you if called by a future prospective employer and see if you can get that in writing, Gordon suggested.
Some clauses in your severance agreement can come back to haunt you later.
"The most important thing is to never under any circumstance sign something that says that you're resigning," said Stern, the severance attorney.
You may think you're saving face by calling a layoff a resignation. But in doing so, you give up your right to collect unemployment, he explained. Besides, there's no shame in losing your job when such a high percentage of the workforce is in the same boat.
But don't stop there. No matter what HR promises you verbally, Stern suggested getting it in writing that your employer won't contest any unemployment benefits you claim, which he warns, is "something that happens every single day."
Then there are non-compete clauses that prevent you from working from your employer's competitors for a certain period of time and, unfortunately, are common in many industries. Although many HR professionals and employment attorneys say non-competes are tough to enforce, why chance it? In some cases, the mere existence of a non-compete can scare away a future employer. So it is definitely something to negotiate away, if at all possible.