How much room is there after an offer? - any advice?

I want to negotiate but I am afraid they will withdraw. I have read a lot of threads here and could not find my exact situation. I have a competing interview next week.

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

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