Are these office 365 account?
Then you can integrate with office365 via the graph connector.
The appstore module below contains some boilerplate micorflows for authentation and calling the rest graph api.
https://marketplace.mendix.com/link/component/117007
Furthermore the outlook calender section in the graph explorer contains sample rest call for making an appointment.
https://developer.microsoft.com/en-us/graph/graph-explorer