Can I use Messages on OS X for two different iPhones with two different Apple IDs? I have two iPhones (one personal and one business), each with a separate Apple ID, so I can keep these logically separated. Ideally, I'd like to use Messages on OS X to be able to send and receive iMessages and/or text messages via both phones. As far as I can see, I can only configure one Apple ID against Messages (in Messages preferences, I cannot add another Apple ID). Is there perhaps a way to run another instance of Messages and/or add my other Apple ID?

I'm on OS X 10.11 and iOS 11, if it matters.
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.