Trying to setup Outlook.com with a custom domain…

I currently have email through two custom domains ([AAA].com & [BBB].com) that are hosted with Google. I'd like to switch over to using Outlook.com for my email. I previously had setup Outlook with the BBB.com domain at domains.live.com. I'd also like to use *** Email address is removed for privacy *** as my primary Microsoft account alias. When I logged in as *** Email address is removed for privacy *** to add this as an alias and switch it over to be the primary, I couldn't add it. The error given was something like "this account already exists."

I had assumed that because I already had the Outlook service setup for BBB.com, I wasn't going to be able to add that address as an alias and use it as my primary alias. So I shut down the Outlook service, and moved BBB.com back to Google for the time being. However, I still can't add BBB.com as an alias to my account.

Long story short… how can I setup *** Email address is removed for privacy *** as the primary account alias for my Microsoft account, as well as use Outlook.com for my email hosting? (I'd like to stop using Google completely, so I don't want to use forwarding or POP access to get the mail.)