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

It is the first offer in 13 months and I do not want to mess it up. It has been a long 22 weeks. The hiring manager was friendly and open. What wording worked?

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

If they say no, consider asking for something else, such as a review in six months.