"All Type Combinations are Possible" is a phrase heard time and time again as a generic and nonsensical reply to any assertion that particular combinations are not possible in typology. The topic is contested and dubious, as the theories such as MBTI/Jung, enneagram, socionics, attitudinal psyche, etc. are separated and no absolute truth of what combinations are possible/impossible is attainable. That being said, this phrase is distinctly anti-intellectual in nature and only poses as an excuse not to actually combat the idea proposed by an OP. I will also be addressing other counterarguments and nuances generally associated with these kinds of discussions.
Now, why aren't all combinations possible? When you read in-depth descriptions for types of differing systems (let us make this easy and compare the description of Se dom/ESxP and enneagram 5 as an example), you can see distinct contradictions in traits of the archetypes presented.
From the Myer Briggs Foundation Site on Se:
"Acts on concrete data from here and now. Trusts the present, then lets it go."
This may be too basic for one's liking. Let us check another site, thoughtcatalog:
"Extroverted sensing is focused on taking in the world as it exists in the present moment. It is highly in tune with the sights, smells, sounds and general physical stimulus that surrounds it. Extroverted sensing lives and thrives in the moment, more so than any other function."
Let us juxtapose this to various passages of enneagram 5 from Enneagram Institute:
"preoccupied with their thoughts and imaginary constructs...detached...have problems with eccentricity, nihilism, and isolation. At their Best...often ahead of their time, and able to see the world in an entirely new way."
"Dealing directly with physical matters can feel extremely daunting for Fives."
"engrossed in this process, they are not interacting with others or even increasing many other practical and social skills. They devote more and more time to collecting and attending to their collections, less to anything related to their real needs."
While my sources may be imperfect or biased, there is a general theme amongst all sources that talk of Se, and all sources that talk of enneagram 5, that list certain distinguishable uniform traits that cannot be denied. That being said, I believe I have made a strong case for disproving the idea of Se dom being able to be a 5 in enneagram. The significance here is that if I have already disproven a single possibility with such ease, then the mantra "All Type Combinations are Possible" has already been shattered. Here is a single counterexample that already defies this silly proposed universal. But this is not merely the only example. While this article is not going to get into each impossible combination, I have already made a semi-decent list of what socionics/MBTI+ socionics/enneagram combinations are impossible. I may describe with detail why particular MBTI/enneagram combinations are also impossible at a later time, with better and refined resources. I intentionally used the sources above for sake of easier communication of my ideas.
Counterargument #1: "The theories measure/describe different things, so you cannot correlate them!"
Indeed, they do measure and describe different facets, but no one was arguing the contrary. MBTI/Jung generally looks solely at cognitive processes, Enneagram looks at pathological motivations, and Socionics measures a combination of cognitive processes, behaviorism, and one's potential social role. However, with a type like Enneagram 5, it is obvious that an MBTI type like INTJ is much more suited to the descriptions with much more ease than say, an ESFP. A socionics LSI is likely to be a xxTJ type. Melancholic types are generally introverted in general. With correlations, we know that the theories are connected in some manner. Many type descriptions of differing systems use similar words and traits to describe different things. Compare an ENTJ/Te description versus an enneagram 3 or enneagram 8 description to see what I mean. To make this absurd counterargument is to say that none of these correlations are possible, positive or negative. An impossible correlation is still a correlation judgment after all; the correlation of having no correlation.
Counterargument #2: "You're just closeminded!"
First, this is merely a pathological argument that obviously does not address the concerns of the OP. Secondly, I would actually accuse this person of Jungian Projection, the notion of attributing one's own fallacious traits to another. What seems more closeminded? Researching all of the theories, reading various descriptions, and maneuvering ideas through one's mind to see what is possible or impossible? Or, merely making blanket statements like "You're just closeminded" and "All type combinations are possible" without any true independent investigation or abstract thought about the matter? This is the battle that these OPs often have to deal with. They were the ones who read through everything, they have the theory on their side (most of the time at least), and did a lot of thinking on their own end only to be met with a generic response.
This response is also often coupled with accusations that the OP is a sensor. And this goes back to the article I wrote previously where typology is being utilized as social leverage as we speak. Malicious and mendacious people will gatekeep intuitive types and use the notion of being sensing as some kind of ideological weapon against people who make arguments that are distasteful to the perceived norms. Not only is it clearly a manifestation of intuitive bias, but it is also a direct admission that one is completely unable to argue against the claims of the OP.
The debates for what combinations are possible will continue forevermore. I disagree with some of the brightest minds in the community over these combinations and we will persist until the end of our tenure in these discussions. However, we should iridescently move past the notion that there are no impossible combinations. Instead, we must address possible/impossible using the theories and principles as our swords and shields in this glorious conflict.