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

I want to negotiate but I am afraid they will withdraw. I worked as a payroll clerk before this. I have a competing interview next week. What wording worked?

Most employers expect a short conversation. Mine did not even blink.

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