I see that your prior Expert opted out of continuing to assist you. It also appears that you asked your question more than a few days ago. I apologize that you were not assisted in a more timely way. Experts that don't have a particular question locked cannot see that question until someone opts out, thus the delay in someone else getting back to you. In any event, I will attempt to assist you.
An employer that does not have a contractual duty to pay severance to employees who are separated, is not required by law to offer any severance. Remembering that basic issue going forward in negotiations is important. That said, if you believe that your employer would be more likely to provide a higher severance if you imply that you might have a gender discrimination issue you would consider pursuing, then you could try to use that as a bargaining chip. However, not all employers would react the same way and you know your employer better than anyone from the outside.
If you do think they would be worried about such a claim, then you could state that you would be willing to waive any right to file suit for gender discrimination (lay out your basis for believing there is discrimination) in exchange for what it is you are seeking from them. The truth is that they will likely make you sign a waiver and release anyway, but if you offer first that might help. You can hire an employment law attorney to negotiate on your behalf if you feel more comfortable with a third party doing this, but just remember that they will take a sizable portion of what you are offered.
As for the amount you can expect, that depends on the practice of your company. If you are an executive, you are likely to be offered more. However, generally speaking, most severance packages start, and often end, at the amount of a range of one weeks pay to one months pay for every year worked. You could also try to negotiate that they pay your COBRA premiums for a certain period as well.
Please feel free to ask follow up questions if you have them. If none, then if you could take a moment to leave a positive rating of my efforts to assist you, I will receive credit for assisting you today. Thank you