Ask HNs: Syncing multiple calendars from multiple domains

Hello! Trying to help a friend and my pre-emptive comment is that that Calendly does not work for him. He has several consulting customers, each of them in a separate domain with their own calendar. Since the organizations are big, they are used to scheduling time using their standard interfaces (GMail, Outlook, etc). It does not work to give them a custom interface (the calendly booking website) and asking them to book through that - this would be an uphill battle. What I am looking for is something that will grab the appts from different calendars and block the time in all of them (without details just showing busy). That way if a customer in Domain A books some time, it will show as "busy" in domain X, Y and Z. I can think of a few ways of writing something custom, but I would rather not. If there is a paid service or some script that I can run in a cron job it would be amazing. It doesn't matter if it is paid or an Open Source script that I need to run manually. How do you keep your calendars in sync?