Does the Booking Engine API support multi-units?

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Same as the Booking Engine, The Booking Engine API supports single and multi-unit properties. However, note the following:

If you'd like to get a list of all the listings using the Booking Engine API, note that you can only retrieve data on single-unit properties and the multi-unit parent unit (and not of each of its sub-units).
To retrieve information about sub-units, you will need to use the Get a specific listing and Get listing availability calendar endpoints.
When searching for availability, Include the checkIn and checkOut query parameters.