Hi,
Cannot be done.
No app on the Mac OS can run in two instances.
Only one Apple ID can be logged in at once in the Messages > Preferences > Accounts > iMessage pane.
You could link the two by adding one email as an Additional item to the other.
However this would mean that all iMessages also synced across all the devices which may be not what you want.
On the Work computer you could set up an Additional Mac User Accounts and have Fast User Switching set up and switch between the two.
Of course both the last two suggestions means your work computer would also have all your private iMessages on the computer.

9:25 pm Thursday; March 17, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad