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

It is the first offer in 13 months and I do not want to mess it up. I do not usually post, so bear with me. I have a competing interview next week. Did it backfire?

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

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