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Yes Zimbra can do this as it is a complete messaging and collaboration suite. If you wanted to brand your installation eg. replace all Zimbra logos then you would need to purchase the
Network Edition. Otherwise you could install the
Open Source Edition. You will require a domain name which has been correctly configured with a MX (Mail Exchange) record etc. If your server was to reside on a internal network eg. private LAN behind a firewall you would need to implement a
Split DNS - Zimbra :: Wiki architecture.