no. regardless of any other factors you cannot bi-amp without two amps.
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If you're asking can you use a stereo amp, one for each speaker and connect one channel of each to the mid-hi, the other to the bass? The answer is yes - provided your speakers are wired to permit this. It's called vertical biamping. I'm doing this in my HT system with 2 Eagle 4's, on on each of my Von Schweikert VR4-III's. The primary advantage is isolating the power consumption of the bass module from that of the mid-hi. I notice better dynamics and resolution. It's subtle, but noticeable.
There are those that say in order to get the full benefits of biamping you need to remove the passive crossover from the speakers and use an active crossover between each of your amplifier channels. This is probably true, though I haven't tried it or compared to the passive approach. Von Schweikert recommends the configuration I'm using. Your results will depend on your speakers.