Offer arrived, can I still ask for more? - first time posting

It is the first offer in 6 months and I do not want to mess it up. I am in Charlotte, in case local advice matters. I have a competing interview next week. What wording worked?

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

Keep everything in writing and save the confirmation numbers. It saved me later.