Offer arrived, can I still ask for more? - 11 months and counting

It is the first offer in 11 months and I do not want to mess it up. There are 5 people counting on me, so I am trying to be careful. I have a competing interview next week. Did it backfire?

Thanks for writing this out. I went through something close to it 11 months ago, and it settled down once I kept a simple log of every call and form.

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