How can I switch a booking from one unit to another (so that there are no empty nights)?

nope that is so not a thing, 

however if you were using a 3rd party channel manager you potentially could.

or you can manually open close the availability on both and just message the guest the correct check-in info for the other listing once they agree to it. 

REMINDER : NEVER POST ANY ACTION REQUEST , ESPECICALLY CANCELLATION REQUESTS HERE, NOTHING WILL HAPPEN., EVER!

Simply report to BdC Partner Support , see below 3 methods.

Message or Call BdC PartnerSupport ***

1. In the extranet, go to the ‘Inbox’ tab.
2. Select ‘Booking.com messages’.
3. Right Pane - Click on ‘See Contact Options’. 
4. Choose Account
5. Now choose Other
6. Then at bottom , See all contact options, and click Message or Call
7. As there is no one number for all partners, the number for your nearest BdC Partner Support is then revealed.

8.  

   *** public main lines via Where you can reach us

    

    

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