Hey Tom,
This is indeed possible, but not something related to The Events Calendar or any add-ons to it. You’d have to make a custom metabox field somewhere in your post/event/page/etc. edit screens, and then just the permissions controls and functions within WordPress to selectively display this field and its data.
Let me know if this helps – if you’re curious about a specific thing here, let me know in more detail and I can hopefully point you in the right direction before closing up the ticket!
Thanks,
George