Offer arrived, can I still ask for more? (Seattle)

It is the first offer in 13 months and I do not want to mess it up. Thank you in advance. I have a competing interview next week. Did you negotiate?

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 made the follow-up calls so much easier.