If it is a large company they have pay bands that limit their flexibility. I would start by negotiating level and research those pay bands. Might be easier to negotiate a one time payment or something that a deviation from their pay structure.
And gather some intel while you can. Get a sense of where you might land in terms of position, pay bands, etc.
Then argue for level first (it tends to be less contentious than money) and if they agree, you've locked in a pay band.