I've tried setting up an additional email domain within Exchange.

I want to continue to receive emails sent to *...@abc.com but also
want to receive emails sent to *...@xyz.com

I've added xyz.com as a new E-Mail address policy within Recipient
Policies. I've updated the recipient update service and I've checked
with my ISP to make sure everything is set up correctly with them.
They've confirmed that xyz.com is set up exactly the same as abc.com
and that their logs show the few emails I've tested as being
successfully delivered to our server.

The problem I've got is that the emails sent to xyz.com are reaching
our server but Exchange is not routing them to me.

Whilst looking in 'POP3 Connector Manager Properties', under the
troubleshooting tab, I noticed that the Exchange mailbox for
undeliverable emails to be sent to was set to Administrator. I changed
this to my own username and tried sending through another email to
xyz.com

The email arrived in my mailbox in Outlook - no problem.

I changed the mailbox for undeliverable emails to another name in our
organisation and tried again. This time the email arrived in that
persons Outlook Inbox.

So, Exchange is seeing emails coming into the additonal domain xyz.com
as undeliverable.

I'd be grateful if anybody could point me in the right direction.