Every lady is going to be different. Most liaisons have a social component to them, and many ladies offer reduced considerations for longer engagements, dinner dates, business functions etc. It really would be best to ask a lady directly if you are looking for a custom package that they don't mention on their website. Some ladies have strictly social rates posted, and for some it is the same (or even more) for public excursions.
It sounds as though you are predominantly interested in ladies at an agency. Some agencies take a percentage of what the lady makes, and some take a set fee for time booked. If the former is true, the agency, if it is one where the ladies are always busy, is likely to have an issue with it because their cut will be lower. If there latter is the case, the lady may not end up making anything, because your contribution may just cover the room fee.
Communication is always key to any good encounter. I really think you need to figure out a way to ask the individual you directly ask the individual you want to spend time with.