How much room is there after an offer? (update)

It is the first offer in 7 months and I do not want to mess it up. It has been a long 14 weeks. 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.

If they say no, consider asking for something else, such as a review in six months.