How should I use Two Step and/or Two Factor authentication with many Apple accounts?
Two-factor authentication

Macworld has a great tip on enabling two-factor authentication for an iTunes-only Apple ID (or any Apple ID not being used as the iCloud account on an iOS device):


Add a new user account on your (or a friend's) Mac.
In the new user account, log into iCloud with your iTunes-only Apple ID.
Enable two-factor authentication (iCloud preference pane > Account Details > Security tab).


It may be a bit cumbersome to switch to this Mac user account though, if you need to manage your Apple ID often.

Macworld also has some tips on using your trusted phone number(s) to receive verification codes when you don't have a trusted device nearby.

Two-step verification

It may no longer be visible in the Apple ID web management interface, but you can still enable two-step verification if you want:


From the Apple Support page for two-step verification, under the section How do I set up two-step verification?, click the link "Set up two-step verification now."; or
Click this link: https://appleid.apple.com/manage/security/2sv/enrollment