Multiple instances of carbide motion

Can I install two instances of carbide motion, one with Bit zero v2 enabled and one without it?

Yes you can. But you have to install it in a folder that is NOT named C:\Program Files (x86)\Carbide
or it will just install the next update to the same folder, without asking you where to install.

For example, on my shop PC, I deleted my C:\Program Files (x86)\Carbide folder and reinstalled V564 (Last version before the big CC format change) and installed it to C:\Program Files (x86)\Carbide564
Then I downloaded V565 and installed it the C:\Program Files (x86)\Carbide565