I know that, as some defenders of MBTI fixed stacks does, you or anyone can advocate that there is a massive mistyping, but still consider this.
You can search members on Typology Central in a way that anyone can counts, for example, how many INFPs the forum has, by simply restricting the search for MBTI "INFP". You can do the same for enneagram. So I focused on 9, which Im unsure of but its likely to be my enneagram, at least for this year, and I searched 91, 92, 93, etc... and had the count.. That searching means that, in 91 example, you will count how many "91" are inside the tri-type people insert, so it counts x91 (random example: 791 tritype) and 91x (random example: 915). Here are the results:
'91' - 2
'92' - 13
'93' - 7
'94' - 20
'95' - 19
'96' - 8
'97' - 10
'98' - 1
And...
'90' - 2 (p90x and 090; more like a joke)
'99' - 0
If you observe some tests that measures all types, you really see the same pattern: People with wing 9 dont usually has 8 or 1 right after.
If any assumptions about 8 and 1 being extremely more compatible than the other wings from 9 are correct, then we would observe '91' and '98' being the most common on the search instead while there would be a very few results from others (which would be more related to jokes as 9w0 is).
Of course, I focused on 9 but I could do it in any enneagram.
You had an interesting idea here that would've worked if it followed how tritype theory is formulated. 91x (or any other permutation of that) is not a valid tritype under the current standardized theory. 98x falls into the same category. Tritype theory as it is defined takes the enneatype of each of the three centres of intelligence (one head, one heart, one gut) that fits your motivations and fears most, not just any arbitrary enneatype. Since the vast majority of people will follow the defined theory, you will not see the vast majority of people of use an incorrect format, thus 98x and 91x will be, by default, the lowest scores. Nonetheless, you will find plenty of people identifying as 9w1 or 9w8, not that that really means anything on my side.
I think a better point that I'm assuming you probably wanted to get at more than this is that people often resonate more with the traits or even motivations/defense mechanisms of other types that, under the traditional theory, couldn't be applied as wings. This is at least where I thought you were going to take the argument. This I would say is a valid interpretation, although I would argue these relations are covered within triadic relations.
All the enneatypes are divided into three different groupings (the centres of intelligence, hovernian triad, object relations) which define traits and motivations which are essential to the types defined within them. As an example, 9 and 4 often relate to one another a lot, primarily because both types are defined within the withdrawn triad, having similar traits of being reserved, introspective, low energy/not starters, generally observers to the world. They even are defined to have similar defense mechanisms, as when faced with stress and their fears, they are inclined to retreat into their inner world and contemplate. Many people, if given the opportunity (as well as, I'd argue, a superficial knowledge of how the theory is constructed), would likely type as 4w9 or 9w4 if a system that allowed for semi-random wing combinations was constructed.
Realistically though, the fears and defense mechanisms individual to the type are not complimentary. The core type defines the main fears and motivations, the wing is added as a flavor, it'd be better to consider it as a sliding scale for how a personality might appear by defining two archetypal manifestations (ie. pure 9w8 or pure 9w1 with no mixing) rather than a type you are supposed to relate to necessarily. In a sense, it furthers how motivations and fears are expressed.
I'll use my own type as an example to provide something tangible that'll lead into a more clear cut explanation (just because it's easier and I'm also a pretty good example), 3w4. I really don't relate to 2 or 4 at as individual types comparatively to other types. By traits and motivations, I would not fit well into either category because I don't fear not receiving or being loved/being unlovable and don't really care in the slightest if I am unique or one who is hidden within the crowd so long as I can pursue and reach my ambitions and goals. In terms of types that I can tangibly see my own personality in, I'd easily type a 3w5 or a 3w1 just because the fear of being incapable/powerless and the fear of being corrupted, are far more important to me than either 2 or 4s fears. Of course 3s fear, of lacking value/being useless probably overpowers both of even those. 1, 5, and 3 are all types defined within the hovernian triads as "competency types," thus they all have similar traits, motivations, and defense mechanisms which link them together. However, despite this, these types are not comparable as wings as it is defined within the theory, I'd argue. 3 and 5 both fear incapability, but go about dealing with that in different ways. 3 is an image type, requiring tangible examples of how they're not a failure, thus are compelled to go out there and prove that they're not one. 5, contrarily, is not. 5s defense is avarice as a head type, retreating to themselves and compiling knowledge do use as as a means of gaining control (ie. knowledge is power). A 3 can hoard information and compile it, a 5 can be focused on external pointers to their control or capability, but in the end, the methodology and motivations the two have do not mesh in the way a wing and core type would. You could say the same about 1 and 3, though I won't throw you through another of my long explanations defining that.
The fears and mechanisms of 2 and 4 however, do compliment 3. To combat feeling unloved, 2 goes out and makes themselves undesposible to others via helping others or becoming what is desirable or lovable. Being lovable or desirable is something that can be acquired and measured tangibly. Being lovable could make someone feel as though they have worth or value, therefore, the fears and mechanisms are compatible. The 3 may not consider unlovable something that necessarily fear, and might rate other fears as more relevant, but the mechanisms of two flavors 3 and are used as "a means to an end." Same with 4, to keep an identity that is identifiable, they cultivate and construct their identity so they are "authentic" and unique comparatively to others, separable. Uniqueness and authenticity is something that can be measured and acquired tangibly, thus, similarly to 2, 4 and 3 have compatible fears and motivations, thus make sense as wings to one another. I certainly don't go around fearing that I'll have no identity (ie. I know I don't have one; I more so fear annihilation which I have confused with 4 motivations back when I struggled to identify my type), but being worth something means exceeding to me, constructing a personality that I value and meets a niche that not everyone can meet.
It's all about compatibly of fears and motivations I'd argue are the biggest things in wings.
There is one thing I get it although... If we were to unrestrict the wings, we would get way too many types (as there are 999 different tri-types although some of them should never happen). Wings unrestricted, every type would have 8 variations, making 8*9=72 different types (remembering that 1w9 and 9w1 doesnt count as the same, the same for every other type).
EDIT: From where I understand, what decides if you are 9w1 or 9w8 is a simple comparison if your 1 is higher than your 8 or 8>1. However, that gives the impression that one doesnt have much traits for other enneagrams, and there are 9w1s with 5 or 7 traits.
I don't think having too many types is a problem in the slightest. No one is exactly alike, so having more degrees of freedom is actually a beneficial thing in making a theory accurate, which is why I'd argue that a model where wings and even tritype fixes are treated as sliding scales in terms of strength are more beneficial that something static, although that's how I thought the theory worked from the get go. I even thing that way about the mbti, although regardless of what form of the theory you use (static stacks, fluid stacks, dichotomes, ect) the theory is too poorly defined to even be accurate in the slightest, although that doesn't have much to do with the enneagram argument and is a tangent that really doesn't have to be addressed.
