Not directly but you could have an alias delivering to the same mailbox and use rules to move them to other folders. Or you can create a shared mailbox with the other email address and give full control to the user so they Essentially have both mailboxes.
As the others has somewhat pointed out, if all you want is a mailbox name that has two different domains, you can do that with one mailbox, and just have the two domains as domain alias'.
I have had clients in the past that did want separate unique mailboxes for each domain however. If that is the case, you will need an separate account for each mailbox. Once you have that however, you can easily just configure your users outlook for both mailboxes.