Can any multi-channel amp be bridged?

You would be better off bi-amping then bridging. Just make sure that your speakers don't have a common connection in the crossover network. Just because you remove the "jumpers" that connect the tweeters and woofers on the outside of the box doesn't necessarily mean that they aren't still connected inside the box via the crossover circuitry. Some bi-wiring terminals are there strictly for looks. Sean
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One of the main limitations of a power amp is its ability to deliver current. If you only use two channels of a six-channel amp, it will be able to supply a lot more current than if it were driving multiple channels.

Even where it's possible to bridge, bridging compromises current delivery and damping factor and therefore sound quality. Bi-amping or tri-amping is best, with one channel per woofer and one per tweeter/mid.

PS. If your amp manufacturer intended bridged operation, there will be a bridging switch and directions on the amp. It's possible to build an external bridging circuit, but I wouldn't recommend it.

When you bridge a stereo amp, you drive each individual amp with the same signal, but one signal has inverted phase. Note that this makes for a more steady draw from the plus and minus power supplies. Some amps (like the Dynaco ST120 of long ago) only meet their specified power rating, both channels driven, when the signals are out of phase. A bridged power amp is operating in a "balanced" configuration. If that's good for preamps, why not for power amps?

I have not used amps in "bridged" mode, but I did do something very similar for many years. I reversed the wires of one channel at the phono pickup, with corresponding reversal of the speaker wires, and then bridged my stereo amp with a center channel speaker. Since most of the signal even in a stereo record, is common mode (monaural, horizontal groove modulation) what I was doing was very close to what today is called bridging. The results were much better than I had any right to expect. Perhaps it was because phase coherency of the three-speaker set was guaranteed by all being driven by the same amp. No amp ever complained about this setup.

So, my conclusion is that, although all the downside comments seem reasonable, bridging can work well. I am sure that 8 ohm speakers are preferable to 4 ohms, but frankly, I didn't have a problem even with 4 ohms. Go figure.

Eldartford, what you were doing with the center channel is not "bridging". In bridging (also called monoblocking, monobridging or summing) a stereo amp becomes a single-channel (mono) amp with much higher power (usually about 3X the rated power).

The setup you described with the third speaker is called a Hafler surround circuit. In a Hafler circuit, the third speaker is fed a left-minus-right signal. Anything that appears equally in both channels is cancelled, and what is left contains a lot of out-of-phase ambient information.

The Hafler circuit was used in the early surround-sound Quad systems with LP. I used one for quite a few years for movie sound, and it sounds fantastic with certain types of music. The Audio Research surround sound system is actually a Hafler circuit. There's a reviewer at The Absolute Sound who uses a Hafler setup for all his listening. NAD gives directions with their stereo amps for implementing a Hafler circuit, but it can be done with any stereo amp. All you need to do is connect the third speaker across the positive terminals of the stereo amp and connect to the positive and negative terminals of the speakers. Properly implemented, the ambient channel should be run at 10dB below the mains.

I've often thought I should go back to a Hafler system for movies. It has some advantages over Dolby and DTS.