Bi-Amping with one amp?

Simple answer, as Eric said, is "yes and yes".
The question is how much benefit you'd get with 4 more-or-less identical amp channels.  Bi Amping has two main benefits that ic an think of offhand:
1. Separate the two loads so if one is demanding or near clipping the other is largely unaffected. Note if they share a common power supply this may not be entirely true. I'm sure the bryston does.
1A. this also often implies just plain more power. Which, all things equal, is always good.

2. Choose amps that better suit each task - good woofer control and lots of power for the bass; less power but "purer" (warning: meaningless subjective term!) sound for the mid/treble.  Might be tubes for timbrel warmth or a small class-A amp, or?????
I have npot had speakers that accept bi-amping for ages. But on an old customer's prodding, i did juts switch from a stereo amp to a pair of (identical) balanced monoblocks with vastly more power and the benefits of E2E balanced.  Its effortless, although at first blush one might say "sounds pretty much the same". It does, only slightly more dynamics, slightly quieter, and when things get loud, ...it just gets loud No drama.
G

"Thanks guys. The question was mostly out of curiosity. Not sure if I will actually try this but it is good to know."  

Even though the amp you wanted to bi-amp with is gone, it's still worth pursuing at some point in the future.  There are some very audible improvements to be had.  

The point is moot now. The Bryston has sold. Didn't even have time to try bi-amping.

...4 channels... only if the speakers you're hooking them up to have connections for bi-wire on the back.

" Active bi-amping is when you have an electronic crossover and it sends signals to dedicated amplifiers. This is almost never done in the home audio, but its done at every rock concert you've ever been to. Good for high sound pressure levels. "
  Active bi-amping is more common than you might think. I happen to be one of them who does this with a Xilica XP3060. It is a PITA to get started with but once learned allows you to fine tune anything. I won't be using passive crossovers in my personal system ever again. On the Klipsch forum there are a number of people doing this and you can search there for what they have done and the results. If you want the very best your components can deliver going active will allow you to do this.

I had a pair of Nautilus 802's powered by a Pass Labs Aleph 5 60 watt stereo. I got another identical Aleph 5 for cheap. Nelson Pass tells me there's no way to use them as monoblocks. So I ran cable from right channel to the woofers and left channel to the mids and tweets. 2 separate cable runs. Same with the other speaker. Only drawback is the channel powering the woofs is doing 90% of the work. So I'd swap the channels once a month. This is called passive bi-amping as the crossovers are still splitting the signal. Active bi-amping is when you have an electronic crossover and it sends signals to dedicated amplifiers. This is almost never done in the home audio, but its done at every rock concert you've ever been to. Good for high sound pressure levels.

Thanks N80, but this is the speaker wiring. What I am referring to is the wiring from the dac or preamp. 

I have a Bryston 5 channel and have been itching to try this with some Vandersteen 3As. The speaker wiring is pretty clear. The source I am struggling with a visual. I assume the white would be split going to channel 1&2, the red split going to 3&4?

Thanks guys. The question was mostly out of curiosity. Not sure if I will actually try this but it is good to know.

Let the games begin! Never bi-amped? Ah, the wonders of alternative systems call to you... 

If you had two stereo amps you would need to decide upon either Horizontal passive bi-amping (one amp dedicated to all bass L/R, and one amp dedicated to all M/T for both L/R), or Vertical passive bi-amp (one amp dedicated to each speaker). 

However, since you have 5 channel, it's a moot point. Use two channels per speaker, as you said. For ease of wiring, keep the channels grouped per speaker, i.e. 1&2 for L and 4&5 for R. Do not try to sum channels. Use them individually, dedicated for each input. 

I haven't looked at the amp, but typically you will need to split the L/R input signals to get your four inputs for the four channels of amplification. Double or triple check connections. Do not do this when tired or drinking. If in doubt, look up a wiring diagram online. 

The real fun is when you begin to ask the question of whether the four channels is better than a different amp's two channels with bi-wire. Correct answer; only comparison would tell. 

Yes and yes.

You can use 4 channels of the Bryston to biamp your Speaker pair.