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

I received an offer as a store manager and I think the pay is a little low. I have a competing interview next week. What wording worked?

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

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