Offer arrived, can I still ask for more? - first time posting

It is the first offer in 4 months and I do not want to mess it up. It has been weighing on me all week. I have a competing interview next week. What wording worked?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.

Keep everything in writing and save the confirmation numbers. It made the follow-up calls so much easier.