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

It is the first offer in 12 months and I do not want to mess it up. There are 9 people counting on me, so I am trying to be careful. I have a competing interview next week. Did you negotiate?

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

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