Adding new iCloud e-mail address

You can add second iCloud mail address say example2@icloud.com in Mac system preferences > internet accounts .

See the articles Use your Internet accounts on Mac - Apple SupportUse your Internet accounts on Mac – Apple Support (AU)

Change Internet Accounts preferences on Mac - Apple Supportsupport.apple.com › en-in › guide › mac-help › mac

Add an internet account - Apple Supportsupport.apple.com › guide › mac-help › mac

The mails from server will sync and can be viewed in mail application Read emails in Mail on Mac - Apple Support

Maximum limit for creating Apple ID from the hardware address of iphone is three , you can't create more Apple ID accounts , however again sign in with your same Apple ID and it's account credentials ( in fact you have signed out the Apple ID ) in the empty fields or sign in with another apple id that was created from another Mac / iPad or different iPhone .

See the article .

Sign in with your Apple ID - Apple Support

Note : you will able to create two new gmail accounts on web because they are not as an Apple ID signed in the Mac , suppose you have used two gmail address and one iCloud mail address , and you still want to create a new mail address with gmail address still you will not be able to create as maximum limit for creating account is three from the hardware address of Mac , it could be with gmail services / iCloud .

The second possible reason you are not able to create account , you have incorrect credentials created for you primary Apple ID set with iCloud domain , for secondary authentication account , you need correct Apple ID password , three answers for respective questions , date of birth , rescue mail address and its password , even one of them is incorrect the new mail address cant be created in upcoming steps , in that scenario convert the secondary authentication account into 2FA Two-factor authentication for Apple ID - Apple Support

rockieslester Said:

"Adding new iCloud e-mail address: I tried to add one new iCloud e-mail address but it doesn't show up when I open Mail."

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Use iCloud Mail:

You can only create one iCloud eMail address. Once created, you not create another on. As for accessing it on another device that is not sign in to your Apple Account, you'll have access it on: https://www.icloud.com/mail