I don't see an option for this within the settings, but is there an advanced configuration somewhere to allow this? If not, add to the wishlist please.
Currently users are able to change the state of their tickets (if the option is enabled) and edit their own notes (if they have this permission). But besides that and adding new notes to the ticket they haven't got any configuration rights. Is there any specific configuration you would like to see for users? We've added this feature to our customer wish list.