Using ASSP with Zimbra
ASSP is most easily implemented with Zimbra as a separate appliance. A simple and modest box running your favorite flavor of Linux will do the trick, or possibly even a virtual machine. Simply configure ASSP to point at your Zimbra host. This gives you not 1 but 2 anti-spam systems. If you prefer to keep it simple you could easily disable the provided system with Zimbra using the Admin console.
A second implementation would be only slightly more complex. It would involve changing the receiving SMTP port in Zimbra to a custom one of your choosing. Install ASSP and configure it to listen on the default port of 25 and specifying in the ASSP configuration to forward to localhost at the custom Zimbra specified port number. In this way both services could co-exist. This configuration is probably more susceptible to issues during upgrades, but reduces the amount of hardware or virtual instances to be maintained.