Here's a thing you need to understand in salary negotiations at competitive, desirable megacorps: the person who decided to hire you and the person who sets your pay are not the same.
Person #1 is your future direct manager or somewhere near him. They likely don't give a rat's ass whether you get paid 120k or 140k. They want the position filled, like, 3 months ago. They're begging HR and the recruiting team to send them qualified candidates to interview. Over the last month they interviewed 2 people who should never have been extended an in-person interview, one person was marginally qualified, and then you came and were qualified and their day was made. So now they want you. Finally, after hours of interviews, they have a live one. You are the prize.
Person #2, the person who you're likely talking to, however, is professionally trained to get you to say yes without going over a given pay range. Depending on the company, their own compensation incentives might be aligned to lowball you as much as they can and still get you to say yes. They literally have no idea what you will be doing, or even what your department does. They just have two conflicting imperatives:
1) getting you to say yes to please your direct manager
2) getting you to say yes for not too much money to please their direct manager
Here's the thing though: it's insanely expensive to hire people. Like, tens of thousands of dollars expensive for the most skilled white collar professionals. And they've already paid a lot of that cost already by interviewing you. About half a dozen people at a minimum were involved before you were extended an offer. Every person that walks away from an offer is a pure loss for them. They really, really want to put a checkmark in the "offer accepted" column of their spreadsheet that's right next to your name.
So now your goal should be, always, to ask for the maximum that you think you can get away with plus some extra buffer just because. What you actually need for your goals is irrelevant. Let person #1 put the screws on person #2 to get to the max number, not the okay number.
How do you do this? You could offer to sign right then and there and start next week if only they would do X. Or email them and explain how excited you are to work on this specific aspect of the role that they value a lot, if only they would do X. Do you notice a trend here? Make it easy for them to say yes. Don't offer justifications from your life's story about your child's preschool schedule, or your sister's upcoming visit next month. State what you want (whatever it may be) and offer something they really really want: a quick fill.
Good luck!