You can only transfer the Priority Date (PD) if you have got your I-140 done with the old company and you maintained the same classification when you filed your

You can only transfer the Priority Date (PD) if you have got your I-140 done with the old company and you maintained the same classification when you filed your new labor certification (LC) with the new company (EB2 -> EB2, EB3 -> EB3 ok, but EB3 -> EB2 not ok). Your last two sentences are spot on... I am guilty of it too.