A more detailed discussion is found in applicable portions of the article at this web address:

http://sound.westhost.com/bi-amp.htm

For even more: http://sound.westhost.com/bi-amp2.htm

If that discussion is too much, and my examples seem either too much or not clear, a simple way of explaining:

1) Feeding two different amplifier channels the same full-range input means each channel is reproducing a full-range output.

2) The output feeding the high-pass crossover filter will have low-frequency current greatly impeded. The output feeding the low-pass crossover filter will have high-frequency current greatly impeded.

3) Since power is delivered only when a voltage is present AND current flows, while each output channel makes all frequencies available, each individual channel delivers power to either the ‘hi’ portion of the loudspeaker or the ‘lo’, but not both at once.

Result 1: This reduces the power ‘burden’ on each output channel, but since each channel is still reproducing the full range, there is no substantial unused headroom in either output channel to allow much increase in power to either the ‘hi’ or ‘lo’ portions of the loudspeaker. As such, there is no substantial power increase available if the same full-range signal is fed to multiple amplifier channels.

Result 2: Depending on the type of amplifier channels being used, sharing the same overall power delivery between two channels that was previously delivered by one channel, and removing the interaction between two portions of a crossover network, might offer some increase in fidelity. In other cases there will be no improvement or maybe even a detriment.

Conclusion: If an overall increase in power is the priority goal, doubling the number of full-range range outputs and feeding them to split two-way crossovers will not provide what is wanted. If you wish for a possible increase in fidelity, you might carefully experiment, see which way sounds better to you.