The Business Class allowance is three pieces unless you have two or more Star carriers on the ticket, in which case, if you are *G then you receive an extra piece.

This assumes that Air NZ are the MSC. Their website has been updated to show this (somewhat vaguely - obviously to discourage people from utilising the allowance). I called NZ today and they confirmed it.

Under "Number of bags included in our fares":

https://www.airnewzealand.co.nz/checked-in-baggage