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

It is the first offer in 7 months and I do not want to mess it up. I do not usually post, so bear with me. I have a competing interview next week. What wording worked?

Keep everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.

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