Same questions as you have.
Thinking out loud ...
Two-Factor Authentication, one iPhone, two Apple IDs. Can it be done?
Simple circumstance, one primary Apple ID for services on multiple devices, but with an additional Apple ID for a second email address.
I primarily use one Apple ID account (AppleOne); for all iCloud services (Calendar, Contacts, App Store, iBook, iTunes, Photos, FaceTime, Messages, Pages , Numbers, Keynote, etc); on several devices: iPhone (iOS 10.3.2), two iMacs (OS X 10.11.6, El Capitan) and Apple TV; but also have another Apple ID account (AppleTwo) that is also used as a second email account concurrently on all devices (without the other associated iCloud services active).
1) Can a single trusted phone number (iPhone) be used to SETUP two-factor authentication for two Apple IDs (AppleOne & AppleTwo)?
2) Can a single trusted phone number (iPhone) be concurrently USED by two Apple IDs (AppleOne & AppleTwo)?
Possible problems: Is Apple associating the unique hardware ID for each device to a specific Apple ID? Do they allow multiple Apple IDs to simultaneously associate to a single unique hardware ID? If not, is there a waiting period to associate an Apple ID to any given device? Are phone service providers (i.e. AT&T, Verizon, T-Mobile, etc) associating the unique hardware ID of iPhones with specific Apple IDs for various services?
If it can be done, logistically how? …
Do I log out of the primary Apple ID (AppleOne) on all devices, removing data from the devices in some instances, and log in under the secondary Apple ID (AppleTwo), to SETUP two-factor authentication for “AppleTwo” on each device?
Once two-factor authentication is SETUP for “AppleTwo” on each device and it is ready for USE; do I log out of “AppleTwo” on all devices and log back in as “AppleOne” on all devices?
After logging back in as “AppleOne” on all devices and starting all iCloud services; would the “AppleTwo” authentication still be valid for the Mail app to USE the “AppleTwo” account email address, or will I have to re-authenticate the “AppleTwo” account to USE the “AppleTwo” email address?
If I do have to re-authenticate the “AppleTwo” account, will Apple send my verification code for “AppleTwo” ID to the trusted phone number (iPhone) even though the iPhone is currently logged in differently with an “AppleOne” ID?
Does the phone service provider know the iPhone has changed Apple IDs and refuse to send it to a phone that is associated with a different ID?
Or do I wait to log out of “AppleTwo” on the iPhone until all other devices have verified the “AppleTwo” email account, and then log out of “AppleTwo” on the iPhone and log in as “AppleOne”?