No, this won't work. With regular amplifiers, the difference in voltage between the AUX input and voltage at the speaker ouput will be too high, overloading the input of the second amplifier, and possibly damage the unit.
At typical levels availaible at the headphone jack you may get away without damaging the input stage of the second amplifier, but due to the impedance mismatch you will likely get excessive hum (noise) and distortion.
The rule that less is more almost always applies. Everytime you pass the signal through another set of cables, switchbox, preamplifier or signal processor, you are adding some additional distortion and noise.
Try for the shortest chain between your source and your heaphones or speakers.
[Source] => [Amplifier] => [Headphones]
Will sound better than...
[Source] => [switchbox] => [preamplifier] => [signal processor] =>[Amplifier] => [switchbox] =>[Headphones]
The fewer links inthe chain, the clearer the sound will be.
If you could drive your headphones directly without the use of an external amplifier, provided your headphones are able to provide identical performance to headphone models that require or at least benefit from an amplifier, this will be the shortest path for the signal and would provide the best sound.
To date, none of the better headphones truly perform well without the use of an amplifier. Also, today's personal portable listening devices can't provide the needed amplification to drive many of the better headphones. Even with today's best available amplifier chip sets, the power supply would have to be too large to be built into a compact portable unit. A manufacturer could build the components of say a Super-Mini headphone amplifier into the chassis of a full sized CD/SACD/CD-A player. But so far none has chosen to do so. I suspect the cost of adding a premium headphone amplifier would be too high to justify building into the unit, as the majority of users would not be willing to pay for this feature.
