Offer arrived, can I still ask for more? - 12 months and counting

It is the first offer in 12 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. Did you negotiate?

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.