Greetings!
This is Tin, to add new email address in to your MS Account, you need to add it as an alias. That's the only way, and to do that, please go to https://account.microsoft.com, log in your account, go to Your Info, click Manage how you sign in to Microsoft, then you can add an email address.
If this is not an option for you, may I know what is the reason why you want to add a new email address on your account so we can check if theres other option?
Thanks,
Tin