Are you working with many Microsoft Accounts? Well, I do. In our company we have tons of Microsoft Accounts (former: Live-ID). Of course we use Microsoft Accounts in all our Windows 8.1 clients, we use some for testing with Outlook and using Skydrive, some for Windows Store Apps, for Phone Store Apps (which Microsoft reunited into one Store Account for Developers at last), for Windows Azure (finally you can use organizational accounts - which are Active Directory users - since fall - before that you needed a Microsoft Account...) and so on.
Despite the fact that working with many Microsoft Accounts is stressy - you need _some_ browsers on your machine to work with different identities in SharePoint, Office 365, Azure and so on - it´s hard to handle. Especially when Microsoft now wants a two factor authentication when using a Microsoft account from time to time.
After the login, Microsoft wants an extra code. If you cannot receive the code (because you don´t get an email, you have no access to the mailbox, there is no mailbox or whatever reason can happen...), you´ve a problem.
The solution to fix this is to add another email-address to your Microsoft Account. This is no big deal - but a little hidden how to accomplish this task.
So here´s a step-by-step walkthrough how to add an extra (alias) email address to a Microsoft Account in the account-webpage. This is also a reminder for myself because I´m seeking around each time when I have this problem, so hopefully this little manual can help you too.
First login into https://account.live.com/.
In my case the Microsoft Account is called dev11. Open your user menu in the right corner and click Account settings.
Open Notifications on the left.
And click Manage email preferences in the middle text block.
In the Profile page you see the preferred email-address (yours). The solution is to add another alias mail address to this account. This - of course - should be an email address where you can receive emails.
Now click Add new address.
And add the second email-address. This must not be a Microsoft Account.
Warning: If you use an already connected email-address it´s not valid:
"This email address is already taken. Please try another."
So you need to use an email address which is not already connected to any Microsoft Account!
Click Add alias. Now you get redirected to Sign In again.
After the login the page Add an alias is presented again. Click Cancel.
If everything worked, now the second email address should have been added to the account.
When we now try to login f.e. on another computer we should get the code input again.
The result is: we get a code to the alias email-address!
Now we can use the code.
So the solution is not complicated but hidden. And solveable.