Multiple Multisite Installs and Dedicated IPs


I'm about to create a multisite (with domain mapping) for a new client, in addition to another multisite install (also with domain mapping) on the same server. I have a dedicated IP installed on my hosting account already. My question is, does each multisite install need its own dedicated IP? Or will the existing one on my hosting account work for everything? I'm using Hostgator if that matters.