Offer arrived, can I still ask for more? (update)

I received an offer as a data-entry clerk and I think the pay is a little low. I do not usually post, so bear with me. I have a competing interview next week. Did it backfire?

Ask about the range, not a number on its own. It felt more collaborative.

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