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To reserve all available spots or options. A noun can be used between "book" and "up" or after "up." Well, that hotel is all booked up, so we'll have to look for a room somewhere else.
book something up
to reserve all the available places. The travel agency booked all the good seats up. Who booked up all these seats?
To reserve all the available places or times, such as seats, rooms, or appointment hours, from something or someone: We couldn't get a place to sit because someone had booked up the entire restaurant. There are only two small hotels on the island, and their regular customers book them up a year in advance. You'll never get an appointment; the doctor is booked up through the next month.