Thanks for the clarification. I agree as to not using an attorney. In most instances an attorney will create more problems than they are able to create benefit for you.
In terms of severance, be aware that the state of NY has no mandatory severance pay law, and an employer may let an employee go without any pay or benefits other than that which has been earned up to the point of termination. On the other hand, if the company has a policy of paying severance pay to employees in your situation, then the employer must treat all employees equally in terms of the amount and nature of the severance pay based on their position in the company at the time of the lay-off.
So if you can show that up to this point the severance package has been based on tenure----or a combination of position and tenure, then you will be in a better position to negotiate a more favorable severance with the employer.
Your best leverage for a complete and fair severance package, if you cannot convince the company to keep you on, would be for you to do some digging, asking questions quietly, and determine the history of severance in the company. Perhaps it is even laid out in the employee handbook, and if so, you know the starting point for your negotiations.
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I wish you and yours the best in 2016,