Bi-Amp ... how about Tri-Amp ?

[Barry]

BTW, a bridged amp is not the same thing as a monoblock. In a conventional amp, one of the loudspeaker terminals is connected to 0 volts (the black one) and the other terminal (the red one) swings positive and negative to drive the loudspeaker. A bridged amp (usually) uses two conventional amps connected together so that neither of the loudspeaker terminals is connected to 0V. Instead, one terminal is driven positive and negative by one amp while the other terminal is driven negative and positive by the other amp. That gives you twice the voltage swing you would have if you only used one of the amps.
In practice this is usually done by using a stereo power amp which has a bridging switch to turn it into a bridged-mono amp. However, it would be possible to do it with any stereo power amp if you also had an outboard device to generate an extra, out-of-phase, signal in addition to the original signal.
Hmmm... I wonder if there's a market for such a device
I doubt it

There are two ways in which a 'stereo', or two-channel amplifier can have its outputs connected together so as to increase the output power:

Series connection - whereby the available voltage is doubled,

Parallel connection - whereby the available current is doubled.

The former option requires a transformer on the input of the two amps, whereas the latter option is possible with amplifiers employing an output transformer with a completely independant winding for the speaker output (that is the feedback is provided by a separate winding). And in the latter case a number of series/parallel combinations might be available, depending on the number of output impedance taps there are on the transformer. For most SS amplifiers parallel connection is easily arranged through using a potentiometer to provide an equal input to each channel.

Quad publish details of how to do this with their valve amps, as well as the 303 and 405 designs. The Quad 510 monoblock amplifier allows various series/parallel output connection with other 510 amplifiers, to provide a maximum power of over 1200W.