How much room is there after an offer?, HR coordinator here

I received an offer as an HR coordinator and I think the pay is a little low. I am in Madison, in case local advice matters. 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.

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