Gain stages: How many in series?

[defaced]

I think answering your question is more a matter of intent than theory.  How much distortion do you want?  That will drive the number of stages.  Sure one can take it to the extreme, but practically there are only a handful of useful answers.  Looking at some classic amp designs can provide some insight into what sorts of sounds you can get from a particular number of gain stages and a given topology.  There tend to be two camps for topology:
Tone stack early in the circuit and plate fed (Fender inspired)
Tone stack late in the circuit and driven by a cathode follower (CF) (Marshall inspired)  
And of these two basic topologies, there are mixes of each that provide their own "flavor" to the mix.  

Twin - two gain stages.  The first one brings the signal up, it feeds a tone stack, and the signal is amplified again.  Because the tone stack is in the middle of the two stages, it's a clean setup.  
Plexi - two gain stages.  The first one brings the signal up, the second clips depending, a CF drives the tone stack.  
JCM800 - three grains stages.  The first brings the signal up, the second and third clip, the CF drives the tone stack.  One of the stages is biased colder to force asymmetric clipping
SLO100/Recto/Uberschall/countless other "high gain" amps - four stages.  Similar to the JCM800, but instead of two clipping stages, there are three.  CF drives the tone stack.
ENGL - four stages.  Just like the SLO100, but instead of a CF driven tone stack, it's plate fed.  TS is at the end of the chain.  
Mesa Mark V - five gain stages.  The first one brings the signal up and feeds a tone stack off the plate, four more provide clipping, and the last of the four drive a plate fed GEQ.  This is like a combination between the Fender topology and the Marshall topology, EQ early, EQ late, and plate fed for all (though that doesn't make much difference for the GEQ because it's actually being driven by NPN BJT transistor (MPSA20)).  
5150/6505 - six gain stages.  The first one brings the signal up, the next five provide clipping, the last of the six stages drives a plate fed tone stack.

So there's alot of permutations of the different number of stages and ways of arranging the parts.  My listening to these amps, you can get an idea of what "universe" each configuration can provide.  But generally speaking with standard preamp design practices (increase high frequency content while also reducing low frequency content early in the circuit, divide down signal between stages to control clipping, and only use the active elements for clipping), the sound becomes more compressed, saturated, and noisy with an increasing number of stages.  Not a very surprising summary, but worth keeping in mind.  

[candidate]

http://www.beavisaudio.com/flash/DS1.html

[Thecomedian]

I like the "buy more DS-1's" analyze

[tca]

I think answering your question is more a matter of intent than theory.  

Thanks for that comprehensive list.

What is missing is the physical "good" device to build the gains stages with all the intrinsic benevolent clipping behavior  And using SS parts in this context IS a completely different story.

Thanks again for all your answers.