Companies do not have to offer severance packages. Furthermore, they do not have to negotiate a greater severance package either. In exchange for the compensation, the company is going to ask for something in return, which is release of any legal claims against the company. If you do not have any potential claims against the company, you should consider taking the offer.
If you are concerned about the release, you might want to have an attorney review the agreement for you and discuss the circumstance around your termination.
Asking for a greater severance package without additional leverage may be challenging. There are, however, a lot factors to be considered, such as the culture of the company, your position at the company, your relationship with the decision makers, and the tone with which you approach them.
Yes, it is possible to negotiate for a larger severance package.
Yes, the company could withdraw the package if is wishes to, unless it is a stated employee benefit.
It is really impossible to tell you on this site whether or not it is a good idea to try.
Some companies have a company policy that extends a severance to certain defined employees, and the benefit is extended in a uniform fashion to all employees that fall within the defined categories. If your company is one such company, it is more likely that it will not negotiate, and it is likely it will not withdraw the offer either.
If you have a valid and persuasive reason for asking for more, I would suggest it be done carefully and respectfully. If your company tends to be negotiators, there may be a better chance of the initial package being an initial offer with expected negotiation to occur. If your company is very black and white in its business dealings, or if the person who will make the decision is mercurial or irrational, then you might want to take the money and run.
Good luck to you.
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If you are negotiating a severance from your employer, you can always ask for more money.
But, the employer is not obligated to give you any severance unless you have some sort of contract.
Whether to hold out for more money is something only you can decide.
We here on AVVO do not know you, the employer, the circumstances, and would have no way to evaluate the possibility of getting more.