Public DNS/MX Question

So I am thinking of installing Zimbra alongside our existing mail server following the split domain article on here. My confusion lies with public dns setup. Right now we have a public address 200.xx.xx.xx which is tied to mail.example.com. The external address is tied to an internal IP with an MX record. Our users email is setup joe@example.com.

For the new Zimbra system should I setup an additional external IP in the same way, 200.xx.xx.xx tied to a separate dns name, mail2.example.com. Using an additional MX record with a lower priority until migration? We want to keep the addresses like joe@example.com.

I am confused as to how this will work, specifically when mail is addressed to joe@example.com how will it know which system to be delivered to if it exists in both systems? Will it matter if it exists in one system and not the other? Will it try both or one or the other?

Am I thinking about this entirely the wrong way? Maybe we could use the same external IP for both systems and somehow tie both internal MXs to it and let the priority of the MX determine where the mail is delivered?