Answer:
I'm not sure there is such a thing as a "common mode amplifier". The common mode rejection ratio (CMRR) of a differential amplifier is very high, and is defined as the ratio of the differential amplification divided by the common mode amplification. The common mode amplification is what you get when both inputs are tied to the same signal. Ideally, this amplification will be zero, but in reality it ends up being some very small amount for well designed amplifiers.
This is a beneficial trait for audio equipment which use a positive, negative, and neutral connection (balanced cables, such as microphones). Noise signals will naturally couple to these cables. The assumption is these noise signals will couple nearly identically to both the positive and negative signal wires, so when applied to the amplifier, this common mode signal will not be amplified, while the desired signal (which is created so that the positive and negative signals are opposites) is amplified.