I know about push-pull amplifier stage, but recently I came to know additional configurations like push-push and pull-pull stages, from a question I was solving. But couldn't find any sources about these stages on the internet.
So do these stages exist, if so how are they built with transistors and what are they used for?
Here is the question. 
A push-push amplifier is an amplifier with two Class-B biased output devices that are driven in such a way that one device gives a positive going output for a positive going input (in-phase or non-inverting) while the other device gives a positive going output for a negative going input (out-of-phase or inverting) and the two outputs are combined so that each half of a sine wave input will give a positive going output (it could also be done with the whole thing inverted to give negative going outputs). It can also be done in other ways such as using transformers to give the necessary phase shifts.
Here's an example using voltage controlled voltage sources and rectifiers to represent the output devices. The rectifiers clip the negative half of the wave-forms to simulate using Class-B bias:
The input signal is inverted by one device:
The negative half of the wave-forms are removed and the two resulting signals are combined and filtered to give a signal with twice the frequency of the input signal:
This can be used in RF circuits to multiply frequencies, for example to get an accurate higher frequency signal from a lower frequency crystal oscillator, and in audio for effects such as creating harmonics from a guitar signal. In RF the devices may be biased Class-C to get better efficiency and/or higher harmonics.
