Multi-amping could have advantages even if done before the cross-overs, and even more so if each channel has its own power supply.
If a speaker has a challenging impedance / phase angle above or below the frequency range of the cross-over the amplifier will often run with more strain and corresponding deviation from ideal performance at these points. A single amplifier channels performance can be dragged down across the entire frequency range by these demands, where as multi - amplified frequency ranges will only be compromised at the particular point of the challenging load, freeing up the other ranges to be powered more optimally. This might be especially true in cases of so called Class A/AB amps where more of the more optimum purported Class A bias will be allowed to run longer before resorting to the less optimum purported Class AB or Class B (these classifications are somewhat nebulous, but the results are somewhat the same).
That these challenging impedance / phase angle loads are more typically found in the bass region where the power needs are greater but where our hearing is usually less sensitive, so meeting the power demands might be more important than ultimate fidelity. On the other hand the power demands of higher frequencies ranges are typically less, but our hearing is usually more critical, and the greater purity of amplification is appreciated more.
