Offer arrived, can I still ask for more? - what worked for you?

It is the first offer in 8 months and I do not want to mess it up. I worked as a data-entry clerk before this. I have a competing interview next week. What wording worked?

Thanks for writing this out. I went through something close to it 8 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.