Can any multi-channel amp be bridged?

Gunbie is right on. Some yes some no some it's amp suicide.
Maybe slow and painful, or instantaneous with smoke and flames!
You MUST find out from the manufacturer if the particular amp can or cannot. (and you CANNOT assume because one amp of a manufacturer can be, that all can be: fatal mistake!
The reason (simplified) is that the electronics must be symmetric in some special way for it to work.

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.