How much room is there after an offer? (update)

It is the first offer in 4 months and I do not want to mess it up. I have read a lot of threads here and could not find my exact situation. I have a competing interview next week.

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.