You have two options to limit the number of appointment bookings per person.
You limit the number of appointment bookings for specific people.
This setting can be found under Contacts > Customer > Permissions.
Here you can select the customer for which service the restriction should apply and to how many appointments you want to limit the customer to per week/month/quarter/year.
Important note: This authorizations are only evaluated if your customers have to log in before booking an appointment online. You can find this setting under Scheduling Page > Settings > Advanced settings > Customer login required.
With the second option, you can determine that all your appointment bookers are only allowed to book a certain number of appointments per day.
You can also configure that an e-mail address may only be used once to book an appointment with you.
You can find this setting under Scheduling Page > Settings > General: