Can Available-to-Promise function any more granular that days?

Hello;

We are a same-day / next-day business and our current situation is that beyond a specific time in the day we do not want ATP to promise anything same-day. What we are seeing is that ATP sees the available supply, and will still promise for same day even though to production may not be until later in the evening.

Any thoughts on how we could work around that? For example, ATP only references current day's supply in a specific set of hours.