Offer arrived, can I still ask for more? - any advice?

I want to negotiate but I am afraid they will withdraw. I have been trying to stay organised about it. The hiring manager was friendly and open. What wording worked?

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 11 months ago, and it settled down once I kept a simple log of every call and form.