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 would rather hear the honest version than the polite one. 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.

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