I would go with questions that are a little more....personable, plus any technical questions about the job that were not answered. You can ask stuff like what are you busy times of year, what problems did you see the last person having, what are their goals for this position over the next year, what departments would you be working the closest with...stuff like that.
Without knowing what the job is, it is hard to recommend questions
But I would continue to show your interest with asking "day in the life of" questions. Almost like you already know you have the job, and are trying to gauge if it a great fit for you.