How much room is there after an offer?, medical assistant here

It is the first offer in 5 months and I do not want to mess it up. There are 5 people counting on me, so I am trying to be careful. I have a competing interview next week. What wording worked?

Thanks for writing this out. I went through something close to it 5 months ago, and it settled down once I kept a simple log of every call and form.