EDIT: The system has been edited to include socionics rather than MBTI
For example,
What if someone cross-typed themselves as an ENXJ. How is this possible? An ENTJ is supposed to have very developed thinking and the ENFJ has very developed feeling. Obviously if your thinking is highly developed, your feeling will suffer and vice versa. Now, let's just say somebody actually was equal in both thinking and feeling. This person becomes what exactly? Their extraverted thinking and extraverted feeling must of been developed equally. How could someone express their thoughts and feelings in the same way simultaneously? That would mean that they have a switch that switches between them. Now, the best way to label this person would be this:
ENFJ(Te)
It simply entails that for an ENFJ this person has developed their extraverted thinking just as much as their extraverted feeling.
Now, this person displays ENFJ behaviour and fits the description perfectly, but has their thinking more developed then it should be.
I have a feeling that what I'm talking about is getting too far-fetched though so I will stop, in my opinon cross-types are basically the flaws of the personality types theory. Even though, it is a very excellent theory, there are a few things about it, especially cross-types that drives me nuts.