Edit calendar invite

At the moment i'm sharing a lot of calendar events with other iCloud users and also receiving them.

What I've always wondered if it was possible to edit a received invite (which I accepted).

For example: I received an invite, I accept and want to add a note or URL to the event in my calendar.

What I can do is access the other persons calendar, because I have read & write rights, and change their event to add notes or URLS, but these changes don't forward to my own version of that invite.