There are several synonyms that can be used for the phrase "book up". One common synonym is to "schedule" or "plan" an event or activity. Another synonym is to "reserve" or "book" a spot or place, such as a hotel room or restaurant reservation. In the context of work or school, "book up" can be replaced with "fill up" or "occupy" one's schedule with tasks and appointments. Additionally, "book up" can be used as a phrasal verb in various expressions, such as "booked solid" or "booked out", meaning that there are no more available appointments or reservations.