Based on my reading of the Mark III schematics on the web, the R2 channel does
not cascade any additional gain stages relative to the R1 channel. Instead, it utilizes more of the gain that is inherently available in the R1 circuit, but which is simply not used in the R1 setup.
For example, the R1 pre-amp circuit is based on the classic
Fender blackface amps from the 60s...in particular the R1 circuit is patterned on the "Reverb" channel of these Fender amps. In this channel, the guitar input goes directly to the first gain stage...then to the tone controls, which causes a the signal to lose a lot of strength, and then to a 2nd gain stage to make up for the losses. After the 2nd gain stage, the signal is sent to the reverb unit. The output of the reverb unit is very weak. So, inside the amp, there is a 3rd gain stage to amplify the reverb output. At this amplifier, it also mixes in a highly-attenuated version of the dry (ie, not reverb'd) signal, so that both signals get amplified together. The "Reverb" knob on the amp controls how much of the reverb signal gets mixed with the highly-attenuated dry signal at this 3rd gain stage.
In the Mark II and later Boogie amps, Mesa moved the reverb unit to be much later in the circuit. They kept, however, the configuration of these 3 gain stages, including the big 3.3M signal attenuator between the 2nd and 3rd gain stage. That's kinda weird, but whatever.
OK, now back to the Mark III...when Mesa designed the Mark III, they created the new R2 channel by partially defeating the big attenuator between the 2nd and 3rd gain stage. This means that less of the amp's gain is "thrown away" by the attenuator. As a result, the channel has more gain overall without actually adding any additional gain stages.
In the Mark III, there are other changes between R1 and R2, but it is my opinion that the partial bypassing of the 3.3M signal attenuator is the most important change with respect to gain. I could be wrong...I'd love to hear other people's opinions.
Hope this helps.
Chip