Negotiating an offer, is it too late? after 10 years as an HR coordinator

I want to negotiate but I am afraid they will withdraw. I have a competing interview next week. Did it backfire?

I thanked them and said I was excited but hoped we could talk about the pay. They came back with a bit more.

Thanks for writing this out. I went through something close to it 7 months ago, and it got easier once I kept a simple log of every call and form.