Offer arrived, can I still ask for more? after 9 years as a logistics coordinator

I want to negotiate but I am afraid they will withdraw. I have been trying to stay organised about it. I have a competing interview next week. Did it backfire?

Thanks for writing this out. I went through something close to it 6 months ago, and it got easier once I kept a simple log of every call and form.

I thanked them and said I was excited but hoped we could talk about the pay. They came back with a bit more.