not much work is done on all three of them but the latest i have seen is on FQAM(Frequency QAM) which combines Frequency and QAM which is a combination of phase and amplitude. For example if you have two carriers and 4QAM one can generate 8 different modulated signals. But what you are saying is something different. Using all parameters of a carrier to generate 3 different signals. A modulator of such kind can be built but the performance of receiver would be not so good due to non-linearity. Any ways it could be an interesting thing to research on.

Few more things. Your question can have two different interpretations.

1) You have one carrier with a certain frequency, phase and amplitude info. From these three parameters you generate three different signals. So your baseband signals comes in and it is modulated by three different parameters to produce 3 different signals.

2) second interpretaion is that u directly produce 3 different signals.

Both the interpretions would have different types of detectors and receiver designs with varying performances.

Thanks Aamir Habib

Frequency and phase modulation are directly related ( not orthogonal) so could only be used for modulating one signal onto a carrier.

A single carrier using its three different parameters i.e amplitude, phase and frequency for modulation of three different signals.

In my view, a carrier amplitude and phase can be modulated simultaneously. But if one has to add to these two variations, one more variation of frequency change, the demodulation process may become difficult. 

We have not come across such implementations.