Is it really necessary? Do you HAVE to have it? I’ve seen heads with up to six 12ax7’s and four or five power tubes, and I’d imagine they’re powerful and produce lots of gain, but why would you need to add a gate if your goal is high gain? Sorry for my ignorance.
My first thoughts about amp design were along the same lines as yours. Want more gain? just add another 12AX7, More power, just ass another output tube and bigger trannies. Then I tried adding a gain stage to an old airline amp. Darn if that thing didn't start squealing, motorboating, and behaving very badly. It's not quite as simple as adding more.
Also keep in mind that each of those 12AX7 bottles have 2 halves. 6 of them could represent 12 gain stages. That is unlikely though. Most likely there are 2 or three in the preamp section building gain for multiple channels and the rest are tone stack recovery, EFX loop, reverb, Phase inverter, etc.
Good distortion harmonics takes a choir of tubes each singing an assigned part. If one singer gets too loud and starts singing over everyone else or starts to get off key, it makes the whole choir sound crappy. The builder is like a choir director. He auditions each tube for his choir and assigns them specific parts, then gets them to all sing together in perfect harmony. The whole is greater than the sum of its parts if done right. If done wrong you end up with an uncontrollable grunting and squealing pig.