Yes. You can set a capacity limit for your service to block a slot when it is already booked.
Here's how to set capacity limits for both existing and new appointments.
Existing appointment
1. Go to “Services”, select on what service you want to allow random day booking.
2. Click on "Availability Settings”, under Capacity Setup, select Capacity By Service and set the capacity as 1. Click “Save”.

Note: You can also set capacity by product, team member, location, or both team member and location.
New appointment
1. Go to “Services” and click “Create New Services”.
2. Enter a service name, select the products, and click “Next”.
3. Next, set up the slot for your service.
4. Block out date & time if needed.
5. On the “Service Availability” page, find the Capacity Setup section.
6. Set Capacity By “Service” and set the capacity as 1.
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7. Configure other settings on the “Service Availability” page if needed.
8. Assign location and team members to your appointment.
9. On the “Review & Publish” page, review your service and click “Publish & Review in Store”.
If you need assistance with setting up capacity limits on your appointment, contact our customer support team.