If you run a crossover before the amps, and bypass the onboard speaker crossovers, there is additional flexibility to be gained - and the ability to more accurately tune the speaker to the room, also if you are running out of steam on the bass, as the bass and treble are seperate amps, distortion generated in the bass amp (harmonics of which would extend into the high frequencies), won't extend to the highs.
Yes there are potential gains to be had - but many of the gains, are benefits that are generated due to the amp(s) being undersized/specced for the speakers.
In my case, there were only marginal gains to be had with the AVR onboard power and biamping, or with similar power external amps... fitting a much higher powered (high current) external amp, provided the same benefits, with a simpler configuration (and ended up cheaper than running a pair of smaller amps!).