I can't answer that one - I personally don't see where a commercial multi student who does not already have a multi on his private can log PIC except when solo.

BTW, FWIW, I think you should be a little concerned about CFI instruction from an instructor who has a poor grasp of the rules dealing with training and what may le logged toward certificate and rating requirements. Hopefully, his instruction is strong in other areas and you know how to separate the wheat from the chaff.