Offer arrived, can I still ask for more?

It is the first offer in 12 months and I do not want to mess it up. I have read a lot of threads here and could not find my exact situation. I have a competing interview next week. Did it backfire?

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.