How much room is there after an offer? (Atlanta)

I want to negotiate but I am afraid they will withdraw. I do not usually post, so bear with me. I have a competing interview next week. What wording worked?

Thanks for writing this out. I went through something close to it last year, and it settled down once I kept a simple log of every call and form.

Ask about the range, not a number on its own. It felt more collaborative.