There a few different possibilities when it comes to creating overlapping appointments. Contact support first to find a solution that would work best for your situation. Below are some ways to how you can get that started:
Allowing Double Booking
If you'd like to allow double booking, triple booking, or more you can change the number of appointments allowed at one time under your calendar settings. Your Calendar Settings page will look like this for any paid account. If you had a free account, you'll be asked to upgrade, since this advanced feature is only available for folks with a paid Acuity Plan!
Allowing Partially Overlapping Appointments
Partially overlapping appointments can be set up within the appointment type. For example, if you're an acupuncturist and only need 20 minutes to work with a patient at the beginning of their 60 minute appointment, you can allow double booking for the last 40min. To set up padding, click the "Block off extra time before or after.." link, and you can add padding to the beginning or end of your appointment there.
Within the appointment types, set the padding after the appointment to a negative number to allow overlapping. In this example set the padding after the appointment to -40 minutes.
That will allow for an new appointment to be booked 20 minutes into a 60 minute appointment.
Contact support if you have any questions.