Yes, you can sync as many calendars as your heart desires simply:
Head over to Calendar Connections > there is a staff top toggle > click add google or outlook connection (works with office 365 too) > follow the authorisation steps, the tick the calendars you would like Cogsworth to read to and tick the calendars you would like Cogsworth to export appointments to.
As an Administrator, you can also view all of the active calendar connections for your business by clicking on the "Other staff members" tab.
Below is a short tutorial on how calendar connections work.
We support any number of Gmail/ Gsuite calendars and Outlook/ Office365 calendars. However as at October 2018, we do not support iCloud yet or self hosted Microsoft Exchange.