If i amplitude modulate an AM carrier with an audio signal, can i then feed that resultant AM waveform into another modulator and amplitude modulate the AM signal to give a signal which is amplitude modulated twice ? I think the answer is yes, then how would you demodulate that ?
Sure, it's technically possible. But I can't think of a reason it would be useful. The resulting modulation would be more complicated to implement, and occupy more bandwidth, than ordinary AM.
Demodulation would be accomplished simply by cascading two demodulators together.
One case where this might happen would be in the world of RF over fiber. In this technique, a radio-frequency signal is used to modulate an optical (usually infrared) signal for transmission over optical fiber. Light is, after all, just really high frequency electromagnetic waves. To the best of my knowledge, the modulation used here is always AM, so if such a system is carrying an AM radio signal then you have AM-in-AM.
Other kinds of "nested modulation" occur from time to time, for instance AFSK as used in the amateur radio VHF packet world is FSK-in-FM.
This would be much less efficient, because the carrier is sent as part of the modulated signal. It also creates a very wide signal with no additional information, so it wastes bandwidth.
Lets assume our original audio is 3 kHz wide and our carrier is at 10 kHz. This is a very low RF frequency, in the audio band. The AM signal goes from 13 kHz to 7 kHz, like this:
USB Carrier LSB | | 13 kHz 7 kHz
Now we modulate a 1 MHz carrier with that signal. We now have an audio signal that goes from 13 kHz to 7 kHz. That audio signal shows up as upper and lower sidebands of the new 1 MHz carrier. It is inverted on the LSB side.
[USB Carrier LSB] Carrier [LSB Carrier USB] new upper sideband new lower sideband | | 1.013 MHz 0.987 MHz
This new signal covers 26 kHz and uses 75% of the transmitter power in carriers and modulated carriers. In the original signal, 50% of the power is in the carrier. When that is modulated again, it only gets 50% of the power in the new signal.
There is a "sideband stacking" technique that is very useful called "subcarriers". This is primarily used in FM broadcast. It is how we get FM stereo, RDS, and over the air Muzak.
The FM broadcast audio feed is about 100 kHz, with bands for mono FM, stereo, and other services. The mono signal is at baseband and the others are translated (modulated) up in frequency.
The diagram in this Wikipedia article shows several common subcarriers.