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 would rather hear the honest version than the polite one. The hiring manager was friendly and open. What wording worked?

Thanks for writing this out. I went through something close to it 13 months ago, and it got easier once I kept a simple log of every call and form.