Back in 2012, Patrick McKenzie wrote Salary Negotiation, which has since become the defacto guide to negotiating salaries for software engineers. It's a great piece and a good primer on how you'd negotiate any offer, including a Staff-plus offer: if you haven't thought about this topic much before, start there.
For much of your career, the offer you get is generated in a relatively formulaic way. Maybe they have a compensation calculator, or maybe they base it off your previous compensation, but it's the company's system driving the numbers. However, there is a threshold where offer negotiations shift, and companies are willing to engage in a bespoke offer rather than a system-driven offer, but you're expected to somehow intuit that you've crossed the threshold--no one will ever tell you.
This sort of bespoke offer starts with more flexibility around compensation, and in particular more flexibility around the equity component of your offer. That said, it's more than just the raw compensation. It's also about other aspects of the offer that the company doesn't generally have flexibility around but is willing to make private exceptions around for senior leaders.
- Their standard contract might give them three months to exercise vested equity after leaving, but they might be willing to extend a Distinguished engineer's exercise window to five years.
- They might not operationally be prepared to support early exercise for everyone but might be willing to make an exception to close a Sr Staff engineer offer.
- They might be willing to offer a deferred compensation plan to support a tax-advantaged payout schedule (this is mostly a thing at public companies).
- They may be open to additional vacation days if they're using metered, as opposed to unlimited, vacation.
- They may support flexibility around work-from-home, working hours, or incorporating in a state or country they don't currently support employing folks in.
It can be hard to know if a given role at a given company is over the threshold, and it's hard to ask the other Staff-plus folks already at the company because it's likely they didn't negotiate these aspects (perhaps because they were promoted from within and never given the opportunity). As a rule of thumb, if a company has more than twenty and fewer than five hundred employees, it's pretty unlikely they are going to do much custom work for you unless you're coming into a quasi-executive role--they simply don't have the operational ability to do so. However, if a company has thousands of folks but only a dozen at your level, it's fairly likely they're open to negotiating bespoke terms.
It's important to be strategic about what you negotiate for. If you hold firm on First Class flights for all your business travel, you might get it, but it'll probably also send a message about your priorities that the company doesn't like.
Whatever you attempt to negotiate, take the time to frame your request in a narrative of why it's important for you. For example, I worked with one senior candidate who framed their request for an extended exercise window in the context of having just bought a house and recently exercising their previous company's equity after leaving. That's a lot more palatable than just asking for more cash compensation. The right narrative gets the negotiation done and does it without generating a negative signal about your motivations.