Is it possible to change Apple ID email and have the old email as 'REACHABLE AT' email ?

I've been trying to do what I described in the title and failed, when I try to add my old email under 'READABLE AT' I get an error telling me that "this email is already in use with another Apple ID.", of course there's no other Apple ID uses that address because I just changed it.

what's strange though is that if I change my Apple ID address back to the old one it will accept, then my new address won't be accepted under 'REACHABLE AT'.

it seems like a bug ?