Items dictated by corporate policy, i.e. weeks of severance, are the least negotiable. But there are many things that aren't described. Items that are within your manager's budget or that that hit a non-cash corporate cost center are more viable than those that need approval from multiple areas or higher up.
An attorney who has negotiated with your local people and division and in your state will have some suggestions. They have a long view and less emotion in the situation. The only goal of HR and legal is to prevent lawsuits. Don't threaten one, or they will become entrenched. Their end goal is that piece of paper acknowledging you accept their offer without any litigation, so keep that in mind and take your time.