I think there's a terminology problem here dealing with the word "balanced".

First, the word is used in dealing with signal transmission (through a cable, for example).
In this instance, an unbalanced signal would be sent on a single conductor with an accompanying neutral reference. This neutral reference is referred to the chassis at each end. Unfortunately, the chassis at each end may not be at the same potential due to various and sundry causes lumped as EMI (ElectroMagnetic Interference).

Balanced signal transmission uses two conductors and sends the signal as the difference in potential between the two conductors. The receiving end measures the difference in potential and ignores any change in voltage that happens to exist between the conductor pair and chassis reference. An additional bonus is that this type of signal is generally sent using a twisted pair of conductors, which adds substantial immunity to magnetic interference.

In an amplifier, there are both balanced and single ended designs. A single ended amplifier uses an output stage that has a single active element that operates between one power supply voltage and chassis neutral reference. This element is usually biased at about 50% of full load current. The output of this device must be coupled into the load with either a capacitor or transformer to remove the (substantial) DC component. Efficiencies are quite low but it's simple.
A balanced amplifier splits the signal into positive and negative halves (assume pure class B for a moment). Each half is sent through a single ended amplifier chain and level shifter, ending up with a pair of output devices, each referenced between a power supply voltage and a chassis neutral. At idle, neither output device conducts. For positive going signal excursions, the device connected to the + power supply rail conducts and places a voltage across the load. The other end of the load is connected to the chassis neutral. Negative signal excursions work the same way except using the negative rail.

With this "balanced" design it is possible to use a signal inverter feeding a second amplifier and connect the load across the outputs of the two amplifiers. As in any case, there will be a tradeoff for this. Advantages include using a lower power supply rail voltage for the same overall output power and cancelling some asymnetry in the output stage caused by using NPN transistors for both sides. Some disadvantages include the cost of a second amplifier, the halving of the output impedance, and the loss of damping factor.

Some conventional stereo amplifiers have the capability to be run in "bridged" configuration, with substantial gain in output power. My Adcom 555 II has a bridging switch that allows it to be used as a monoblock at 600W/8 ohms or 800W/4ohms instead of the 200/8 and 300/4 normal ratings for stereo operation.

Steve
In real life, an electrical engineer.