I found an way interesting way of looking at supervision, which is that quasi-types are always supervised by an activity pair.

4D Ti/Si is supervised by Alpha Extrovert
4D Ne/Fe is supervised by Alpha Introvert
4D Ti/Ni is supervised Beta Extrovert
4D Fe/Se is supervised by Beta Introvert
4D Ni/Fi is supervised by Gamma Extrovert
4D Te/Se is supervised by Gamma Introvert
4D Si/Fi is supervised by Delta Extrovert
4D Te/Ne is supervised by Delta Introvert

The reason I think looking at it this way is interesting is because I think there are themes that can drawn here. Activity types, even through they operate in opposite fields, have similar missions that in a way "defeat" a certain pair of strong functions. I'll give examples:

The spontaneity and outward emotionality of alpha extroverts supervises the rigid calmness and reserve of Ti/Si.
The ability to of Alpha Introverts to create and maintain harmony supervises the manipulative needy attention-seeking nature of Ne/Fe.
The ability of Beta Extroverts to climb high on the social ladder and show off power supervises the typically uncharismatic and minimalistic Ni/Ti.
The idealism and rule enforcing of Beta Introverts supervises the chaotic Fe/Se.
The ability of Gamma Extroverts to play by the system and use it to their advantages supervises the naive, overly idealistic Ni/Fi.
The tendency of Gamma Introverts to judge one's character supervises the harshness and lack of empathy in Se/Te.
The knowledge/experience amassing of Delta Extroverts supervises the bubbled lifestyle of Si/Fi.
The ability of Delta Introverts to focus their efforts towards the few important things supervises the endless expenditures of Ne/Te.

So looking at this way we can easily see how the missions of the supervising activity pair supervises the tendencies of the supervisee quasi-pair.