Negotiating for a higher severance package implies that the existing severance package, or absence of a severance package in the first place, are not congruent with what you think it should be. As such, you’ll need proof to make your case for what it (the severance package) should be. Collect evidence to support why should get a better severance package and why it would be beneficial not just to you, but to all parties involved (including the company). It’s hard to argue with facts and figures. Or if it’s a situation where there’s one specific situation that has given you leverage, confirm how solid your leverage is before entering the negotiations. In other words, get legal advice where applicable.
Having good facts and figures only gets you so far if you fall flat when presenting the information to the key players. Being able to maintain good working relationships in a stressful environment, having patience and being able to persuade others without using manipulation will increase the likelihood a tough negotiation will end closer to how you would like it to. Just remember that there are bound to be conflicts or problems in the middle and that the best solutions revolve around collaboration and problem-solving, not competition and a blame game.
Be honest and ethical during negotiations to inspire the same from the other side. If you feel like you are not getting the same from the other side, let them know. If your concerns go unheeded frequently enough, perhaps suggest a third party attend the negotiations to keep everyone’s interests balanced and improve accountability of the process overall. For situations where you are lucky enough to have a company with outplacement services, be sure to confirm your eligibility for such services. If no outplacement services currently exist at your company, mention how difficult the transition is going to be for you and ask for them in a one-off scenario.