Linking two accounts via aliases

I have a personal hotmail account.  I recently created a new outlook account for business.  I can't open the two together because the 'system' reads them both as me.  Then I found out about linking accounts via aliases.  So I tried to link the outlook account to the hotmail account under the 'add existing account' heading but it keeps telling me the outlook account is already taken.  Of course it is!!!! It's an existing account.  Is there a way around this?