You can change your ID for iCloud? Perhaps, but not to an existing iTunes ID.
Example: I logged into iCloud, clicked my ID. Clicked Apple ID. Which takes you to:https://appleid.apple.com/cgi-bin/We...MyAppleId.woa/
Then you 'manage your account'.
Apple ID is unchangeable.
Primary Email Address is changeable, but if you use an existing Apple ID email address you get:
"Email address is already verified for another Apple ID."
So, I don't see what you are talking about.