Amps in sequence....

Okay, let me state that I've not done this. I am just asking, mostly out of curiosity. After reading about about Vandersteen subs use the feed from an amplifier to generate the signal for the sub's internal amp, I got to wondering why or if it is possible to use weaker amps in sequence? In other words, take a weak amp's signal and feed it into another power amp to amplify the signal? I've never heard of this, so methinks it is a very bad idea, so I'm just curious why?

There was an amp designed to do just that. The "supercharger". (I foget the brand "M" somthing?)
They were 500 or 1,000 watts per channel and were to be hooked up after your small amp.
That was the Musical Fidelity Supercharger, advertised to boost the power of your amp to the speakers while preserving the original amps sound.

Similar car stereo power boosters used to be popular years ago.

Newer Class D amps can achieve similar power levels in a small and energy efficient package that is also often quite cost effective.
This is done with some other subs also.If your power amp is full range,that is supplying the bass needed,they don't seem to think there's a problem.
Subs which have their own amplifier, and have speaker-level inputs, draw essentially no power from the main amplifier. They are designed to accept speaker-level voltages, which are much too high to feed into a normal power amplifier input, and to generate the high current and power levels required by their driver, in proportion to that input voltage.

To put two amplifiers in series, you would have to provide a means of reducing the voltage levels coming out of the first amp, or have the second amp specially designed to accept higher than normal voltage levels. More significantly, in either of those cases the power generation capability of the first amp would be completely unutilized and wasted, and the power level that could be provided to the speaker would be the same as the power capability of the second amp.

Equipment which has been available to provide a means of putting two amps in series typically addresses the situation where there is an underpowered receiver, and the user wants to connect a separate higher powered amplifier, but the receiver does not provide preamp-out jacks to connect to that amp.

Another problem that would arise is that an amp that has output transformers, such as most tube amps, should not be operated without a speaker load or equivalent resistive load, or damage can result. Therefore a dummy load, such as a high power 8 ohm resistor, would have to be provided, either internally in the second amp or externally. But again, the power generation capability of the first amp, and the expense that represents in terms of hardware, would be wasted.

-- Al