Yes, in most cases you can book more than one room at the same hotel in a single booking. When you search, you tell the system how many rooms you need and how many adults and children are staying in each one, and the results come back priced for that whole group. You then get one booking reference covering all the rooms, which is much easier to manage than juggling several separate confirmations for the same family or the same group of colleagues.
There are a few things worth knowing before you rely on it. You will usually need to enter a lead guest name for each room rather than just one name for the whole booking, because the hotel needs to know who is checking into which room. The rooms do not have to be identical, so you can mix a double and a twin if the hotel has both available, but the price can be different for each room and you should read the figures room by room rather than assuming they are all the same.
The limits here come from the supplier, not from us. Many suppliers cap how many rooms you can put in one booking, and once you go past that number it is treated as a group booking that has to be arranged separately with the hotel. Cancellation rules can also differ, as some suppliers let you cancel one room and keep the rest, while others treat the whole booking as a single item that can only be cancelled in full.
Before you confirm a multi room booking, check the cancellation terms shown against it and make sure they say whether rooms can be dropped individually, so you know what you can promise your customer.