I'm a little late to the discussion, but here's my take:
There is the very real condition of channel crosstalk!
So, if you use one St-10 for both woofers of the two channels, the crasstalk would result in "less than perfect" stereo, but nothing harmful.
If you use one St-10 L channel for the woofer and the R channel for the tweeter of, say, the left channel, the crosstalk between channels will "pollute" the base frequencies with the higher pitched ones, and viceversa. If you no longer have a passive after that point, this could cause, at best, distortion on your speakers, and at worst a lot of damage.
So, with two amps, do biamping. For independent left and right amplification, you will require 4 monoblocks, I'm afraid.
That's my educated guess, anyone is free to prove me wrong and I am happy to learn!