How much room is there after an offer? - 13 months and counting

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

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.