Customer Double Booking

I have no idea if my explanation will make sense but here goes...
We are using the plugin for parents evening appointments.
We have staff and parents.
When a parent books an appointment for 'Teacher A' at 3.00pm it is set as occupied, great. However that same parent is able to book and appointment with 'Teacher B' at 3.00pm.
So my question is, can you block out a customers time as 'busy' - so it is almost a reversal of employee busy?
Really hope this makes sense to someone!

If you've set up your teacher-parent event as a single event with the option to select the teacher that the parent wants to meet within that event, then there is an option in [EventBooking -> Congifuration] for [Prevent Duplicate Registrations] which will prevent the same user from registering for the same event. You'll need to make sure that your parents are registered with the site in order for this to work.
If you have different events for the different teachers, I don't see any option that would prevent the user from booking overlapping events. I thought I saw that option within the component, but can't find it now -- it probably was a feature in the component that I was using previous to joining the Event Booking club and I am getting the two mixed up.