Can I use Messages on OS X for two different iPhones with two different Apple IDs?
Depending on how committed you are, you could install a virtual machine on OSX and from there login to your business iTunes account. Furthermore, it's possible to drag just the iMessages application (from the virtualized OSX instance) to your Dock giving the impression of running two different iMessages accounts simultaneously.

I've accomplished similar tasks using VMware for Mac, but Virtual Box may be a good free alternative.