Hello @Hannah177,
You can list on as many platforms and in as many other ways as you wish.
You must take care to avoid double booking situations. To this end, it's better if you don't have instant book turned on on Airbnb.
Having that off allows you to check your existing bookings to make sure that a new Airbnb request can be accepted without causing a double booking.
You can synchronise your platform calendars to help avoid double bookings but remember that the synchronisation is not immediate. It can take up to a day for activity on one calendar to appear on ones synchronised to it. So don't rely on it solely.
How do I sync my Airbnb calendar with another calendar?
As is all too common, the instructions at the above link are only mostly right. Skip step 4 in the "Import calendar" section. Airbnb frequently changes its user interface without bothering itself to help people by updating its help articles accordingly.
Steve.