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

It is the first offer in 2 months and I do not want to mess it up. I do not usually post, so bear with me. The hiring manager was friendly and open. What wording worked?

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.

Keep everything in writing and save the confirmation numbers. It saved me later.