Is there a way to synch "private" calendars?

I’ve got a multisite with several private blogs (you need to login to few them). Each of this blogs uses its own calendar.
I need to synch them with the calendar on an also private blog.

Using the normal way of importing the calendar-url into the calendar feed fails, because the calender isn’t a logged-in user.

Any idea how to solve this problem?

https://www.ads-software.com/plugins/all-in-one-event-calendar/