Right now when I, account owner, am cloning a project, I only have permission "Clone custom and system fields", and the values also are being cloned.
I'd like to have an option to leave the values empty, if they're not related to the new project.
Like two different options:
"Clone custom and system fields"
"Clone values in fields"

Similar to what you have for user groups:
"Clone groups and Issue workflow
Clone Users in Cloned groups"