Sorry you are incorrect, Only in Class A is the whole of the signal contained in the operating area of the transistor, thus only class A amplifiers transfer the whole of the original signal on to each successive stage.
Class B C and D chop more and more out of the crossover point out of the signal as it passes through each stage.
That used to be true, but it seems class D has got quite good. This prompted me to look up the old LM12 but I cant find it anywhere but Ebay. Must be out of production.