What model of speakers are you planning to bi-amp?
Why not upgrade your AVR?
Most of the advantages of bi-amping can be had by using a single more powerful amp for each speaker assembly: most of the power is needed by the woofer. The power needed to drive tweeters and midrange drivers is miniscule in comparison.
Bi-amping is often needed when using tube amps -- then usually have limited power and limited bandwidth. It's not needed at all when using modern high-power, wide-bandwidth, solid-state amps.