Why is it that we are able to combine Amplitude and Phase modulation (Resulting in QAM) but are not able to do so with frequency? Why not combine all three degrees of freedom (Amplitude, Frequency, Phase) for modulation?
Quadrature amplitude modulation could be viewed as a combination of phase and amplitude modulation, but it could also be viewed as overlaying two amplitude-modulated signals that are 90 degrees out of phase and have a limit imposed on the sum of the squares of their amplitudes. If one interprets the signal in such fashion, and has a reference waves which are at "zero degrees" and "ninety degrees" phase, one can multiply the incoming signal by those two waves and filter the result to get the zero and ninety-degree components.
While it might be possible to combine frequency modulation with amplitude modulation, many techniques of detecting frequency-modulated signals have gain which will vary slightly with the incoming frequency. Thus, even if an FM signal was transmitted at a uniform amplitude, the output of an early stage of the tuner might have an amplitude that varies in response to the modulating signal. If the amplitude of the signal at that point is going to be ignored, that's not a problem, but if one is trying to recover an amplitude-modulated signal on top of the FM signal, one would have to filter out such effects.