Hi,
Thanks for the interest in Events Calendar Pro.
That is an interesting setup. We do not support anything like you describe out of the box.
But you maybe to get something working.
Option 1
Set the personal engagement events to Private. They will not show in the Calendars then, however, they may not show even for logged in users.
You could test this with the free version of the Events Calendar on WordPress.org
The Events Calendar
Option 2
One way that might work is to create a category for the Personal Engagements and then remove those events on the front end if someone is not signed in.
There are some snippets already available to remove events by categories.
We could help you get started with that, but for the most part customizations are beyond the support we can provide.
Let me know if you have any follow up questions.
Thanks