When a multi-part service is booked by a customer it will appear on your calendar with the layered multi-part booking icon:
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You can change and modify the service as a whole by clicking on either of the service parts and then clicking View booking details. 

You can edit, cancel, add additional customers, add a note etc. to update the booking; just as you would with a standard service booking.

To change the time of the booking you can either follow the steps above and click Edit booking, then change the date and time, or alternatively you can drag and drop the booking to another day or time.