In order to accept delivery for a given domain, you must have a recipient policy for that domain. Let's say mycompany has registered the internet domains mycompany.com, mycompany.org, and mycomapany.net. All three have MX records in External DNS that point to the same Exchange server. The internal AD domain is corp.mycompany.com. The default recipient policy stamps each user with user@corp.mycompany.com. To recieve mail sent to user@mycompany.com, user@mycompany.net, or user@mycompany.org, you would also need address rules within the recipient policy to create the additional addresses. You would probably want to make user@mycompany.com primary if that is the address you want the real world to see.
Often times it is also useful for a user to have multiple smtp addresses in the same domain. One example would be to have both user@mydomain.com and position@mydomain.com. Other times, additional email addresses are added for the sake of convienence.