How would XXXx work? How would they choose which type to be? For what purpose?
First of all, let's discuss a fictional account of type change.
To begin with, I don't think most people can type change. The reason for this, I surmise, is that most people have an inner sense of their own duality. So long as they can get information, they can continue to "prop up" their functions. (or keep them in place, as the case may be, by cutting off their information flow). But what if you didn't think you could get duality from any place save one? What if you could be convinced that all the goodness in the world had been expunged? Without hope, what would you become?
I surmise that your alter ego would take over, putting its most powerful element in the lead. I think that this would amount to dissociative identity disorder, or as we think of it here, type change.
That's involuntary type change, the sudden loss of one's own personality, a loss of one's own self-identity and the creation of another. Think about it: how could you possibly reconcile having absolute confidence in an element besides that of your base? "Well, at one point I believed in this... then I believed in this." You couldn't, because you couldn't justify the foundation of your identity to that point. What if everything you knew about yourself was wrong? Thus, there would be nothing to keep you from assembling a new identity from the same base of information. (your memory) Yet, your identity would necessarily be different, because it would be anchored on a completely different set of axioms. It would follow that a socionics aware person would be in position to offer superior treatment for DID. (after receiving appropriate training).
The next step is considering what would it be like for a person to voluntarily change their own function order. First off, this would be kind of stupid: we all know that the function order exists because each of the elements is tied to a function, and that if we try to use them out of order them we're going to make asses of ourselves. (and if it's in dispute, Huitzi is on hand to affirm it). At the very least, we won't have a whit of self-confidence in what we are trying to achieve. Granted, we don't know the details of how acting against type manifests (the wager of stupidity), but that's not the point of this discussion.
Maybe the XXXx would be a really insecure person who felt that all of their functions had to be protected. Perhaps they would feel it necessary to shore up the integrity of any function at any notice. For example, if Ne is getting squandered, then wouldn't you want to use Si to nurture it? There's a great deal of lattitude for exploration down that particular road. It's also possible that there is an XXXx in each of us, and that by denying the constancy of type we are in fact getting in touch with that side ourselves. Perhaps XXXx is the observation that possessing type limits our capacity as individuals, and thus creates in us an instinctual urge to deny our limitations.