Hi,
I have an Apple ID that is based on a dial-up account I once had.
It also has a recovery email linked to this.
In addition when iCloud Started I linked it to iCloud and originally got an @me.com ID as well and later an @iCloud.com one as well.
I also have several other Apple IDs (mostly @mac.com com IDs gained for iChat during the MobileMe period) and I have removed the linked/recovery email from these to create new Apple IDs (you do eventually run out of emails to use). So I know it can be done.
However my regular Apple ID is also inked to my posting ID here at Apple Support communities.
I was once able to change the email from the Apple ID one to another for my email notifications but still list another in my Profile for direct contact.
I am not sure which is causing the issue but I find I can't follow the instructions that you are supposed to be able to use to "change" the Apple ID.
I certainly can't make it the @me.com or @icloud.com IDs (it says I can't use another Apple ID when they are in fact already part of this account).
I also see that the Profile here now forces you to use the Email for notifications and not anything else. (this might depend on who and where they are looking).
You can of course use the iForgot site to check if it just happens to be linked to another ID.
9:11 pm Sunday; June 29, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad