This is just something I thought up from experience:
I'll quickly explain the premise. I know some of us here are into MBTI/Socionics as it is, though I was thinking of a clearer categorization for people, that deals with the fact that all four types within a quadra have the same values and get along the best, but all four come from different sets of strengths: namely the reknown NT, NF, ST and SF stereotypical clubs that I think many of us see a clear delineation in. Ie. in theory there would no longer be two types of NTs, but four types of NTs, + four types of NFs, four types of STs, and four types of SFs, and they each differ in emphasis and cognition and each value things more similar to their quadra, each according member of the other three clubs. If you're NT you still have their behavior and strength overall, you just aren't typical "NT" anymore and you belong to your own unique subclass of NT. Or your own unique subclass of NF, etc.
This idea would seem to fit people in real life pretty well, and if we were to have a good set of descriptions per each "club" and each "quadra" then we could make further observations about the four different club members, and each different quadra member. This theory revolves around the realization that you have values in common with people of all four clubs, and given the correct outlook as to what those values are, these ideas may be implemented closer to the 16 types as they are, but more than that, they can seriously be taken to form something twice as intricate about personality types than what we know now, and all from the same mental practices we're familiar with.
Instead of necessarily saying there's already an NT Beta type, which leads one to think of where there is an NT Delta type, etc, perhaps the best way to construct this is to look at NT types as a whole, and from there begin to acknowledge four various subclasses of NTs we may begin to clarify. The quadra emphasis comes after the fact of making these observations along with some usual quadra observations, but there is twice as much room now to allow for more conceptualization besides the 8 information elements alone. One must think ie. if one were a subclass of NT, wouldn't one's ego functions differ to some extent from the other three?
The advantage of using any forum to construct some observations is that everyone makes these observations already, that within a club of NT types, as well as the other clubs, it often seems like there are more than two value-sets going on, and one cannot expect to relate well to half of the people in their club than they can as much one-fourth of them. The "quadra" emphasis needs not to be as obvious as the differentiation within each club, but only be an after affect which appears to place four type values in alignment. So perhaps noting the stark color difference within each club is the most important aspect of the graph.
The organization of it would look like this: (without necessarily the old quadra names, but quadras that fit nonetheless)
There are four main Socionics and MBTI dichotomies. Two of these, N/S and T/F, when combined form one of the two "four-preference" dichotomies used in this theory called the "club" (the other being "quadra.") Here are some possible short-descriptions of the four clubs (taken from an old test):
The Pragmatist (ST) - His focus is on productivity, function, achievement, efficiency, effecting change, building, engineering, business, and/or acquiring power. He's pragmatic and seeks to improve his individual position.
Pragmatists (STs) share more in common with Researchers (NTs) and Socials (SFs) and have the least common with Humanitarians (NFs).
The Social (SF) - He cares about people, making connections with them, and interpersonal interactions. He often enjoys hosting and going to parties, gossip, familial interaction, and other types of activities that value or emphasize socialization.
Socials (SFs) share more in common with Humanitarians (NFs) and Pragmatists (STs) and have the least in common with Researchers (NTs).
The Humanitarian (NF) - His focus is on the greater societal needs and problems; often has interests in philosophy, art, psychology, sociology, and/or politics. He's humanitarian and seeks to improve society.
Humanitarians (NFs) share more in common with Socials (SFs) and Researchers (NTs) and have the least in common with Pragmatists (STs).
The Researcher (NT) - His focus is on researching areas of interest. He often puts much thought and time into an area of interest, finding information on the topic, making conclusions and deductions, and then presenting these plans, hypothesis, theories, and predictions. He values understanding and knowledge with less emphasis on either his personal benefit or society's.
Researchers (NTs) share more in common with Pragmatists (STs) and Humanitarians (NFs) and have the least in common with Socials (SFs).
As far as what quadras can divide these further up, even at their individual level, is still in question, though it may easily be the quadras described within Socionics (if not something better).
So the idea essentially takes the NTs, for instance, and looks at the unique differences within them, and instead of grouping ENTPs and INTPs together with simple differences in introversion and extroversion and their given correlations, it ignores these types and sees four unique types that are different from one another: xNTx 1 is simlar to xNTx 2 is simlar to xNTx 3 is simlar to xNTx 4 is simlar to xNTx 1.
One might have more introverted tendencies on average, or more P tendencies, who knows (just how N types have more P tendencies on average; it's all correlation) but we try to arrive closer to the essence of personality.
So what observations can you make about four unique types within your club, from your experience?