There are many ways to make a group of people diverse without giving them overly specialized roles within an ensemble. One way is through matching personality types according to a wacky ancient pseudoscience. The four temperaments (also called the "four humors") was a theory that behavior was caused by concentrations of body fluids — the "humors" of classical medicine: blood, yellow bile, black bile, and phlegm.
A temporary imbalance would create an illness: too much blood caused a fever, too much yellow bile caused a cough, too much black bile caused depression, and too much phlegm caused a cold. A permanent imbalance led to a person having a certain type of intentions, behavior, and personality. Though this theory has long since been discredited from a scientific standpoint, the general idea still remains and the theory is still used for personality profiling. An ensemble based on these four humors can make the cast diverse without actually changing the roles of the characters in the story.
The four temperament system was an interesting one, but flawed. Several tests noticed people that did not conform to any of the behavior types, so a neutral temperament was created. Along with a sampling of related tropes, the five temperaments (humors) are:
Leukine (white plasm): Ambiverted and dually-oriented. The "central" temperament that was created for those who didn't have one of the four clearly-established temperaments. This type of character can generally be described as middle-of-the-road and neutral. Tends toward either true apathy or rotating among nearly all the world's emotions (nothing too explosive or extreme) at a smooth, gradual rate. In a positive light, having more than one temperament or balanced among temperaments; but in a negative light, a non-temperament, The Generic Guy, and a Standardized Leader. Usually reserved for protagonists, The Hero or other leaders when they are neither Hot-Blooded nor emotionless characters, and somewhat more independent but not as introverted.
Phlegmatic and Sanguine (the Guardian): Ambiverted and people-oriented. The temperament combo that thrives most on relationships with other people and is the most emotionally strong for other people. Usually the most easygoing and least judgmental; and, as "Guardian" suggests, supportive and helpful at guarding a team or family from falling apart. On the flip side, often overly tolerant and/or permissive; often sluggish about any task that requires spending a bunch of mental energy. Often evaluates other people in a very optimistic light, an overlap of The Pollyanna and the Wide-Eyed Idealist (distinct from the above "Idealist"). Usually the diametric opposite of an Insufferable Genius or Neat Freak. Taken to an extreme, can be a Cloud Cuckoolander.
Historically in plays, there was a whole genre: Comedy of Humors, where the impetus of the story is the sudden banding of these opposing types. This is in contrast to the Comedy of Errors, where the story is driven by the events and situations.
Sometimes a Five-Man Band will also be a Four (or often Five) Temperament Ensemble, but in many cases, they're mutually exclusive. There is also some overlap with Power Trio scenarios: usually The Kirk is choleric, The McCoy is sanguine, and The Spock is melancholic. In these cases, the phlegmatic role will be filled by a prominent supporting character, who is still clearly outside of the triad. They are also similar to the four Personality Blood Types, and are sometimes also a Four Element Ensemble.
If this type of personality dynamic is used for a Five-Man Band, then there are — aside from The Hero as leukine and The Chick as phlegmatic — two very common sets: either The Lancer (choleric), The Smart Guy (melancholic), and The Big Guy (sanguine); or The Lancer (sanguine), The Smart Guy (choleric), and The Big Guy (melancholic). RPGs in particular like to use a simplification of the second type.
See also Cast Calculus for the overarching archetypes in this and differently numbered ensembles. Here is an Image Archive for this trope. Additionally, Pseudolonewolf (of MARDEK fame) has a page that goes into great detail on the four temperaments, here. For another way to split up a group of four, see Four Philosophy Ensemble.
Ed Wood, despite being a biopic, gives us four well-defined examples: Ed (sanguine), Dolores (choleric), Bela (melancholic), and Bunny (phlegmatic).
Roy's subordinates in the Elemental Chess Trilogy have similar assignations to those given in canon, but not identical. According to here: Havoc (sanguine), Breda (choleric), Fuery (phlegmatic), and Falman (leukine).
In Point Of Succession Matt (sanguine), Light (choleric), Watari (phlegmatic), and L and Near (melancholic).
Intentionally invoked in Promethean: The Created. The five Lineages of Prometheans are Frankensteins (choleric), Golems (melancholic), Galateids (sanguine), Osirans (phlegmatic), and Ulgan (associated with the "humor" of ectoplasm.) The character's balance of humors is actually an important gameplay point.
Also invoked in Tribe8 with the monstrous Z'Bri, whose 4 types are named after the four humors (of the old model): Koleris, Flemis, Sangis, and Melanis.
While FATAL does have a humors system, there is no rule forcing your party to be a Four-Temperament Ensemble. Indeed, this would actively contradict the obsessive randomisation inherent to the FATAL system.
In Warhammer and Warhammer 40,000, appropriately enough, the four gods of Chaos each represent an emotion and mindset. Khorne (the god of anger and bloodshed) is choleric; Slaanesh (god of passion and lust) is sanguine; Tzeentch (god of ambition and hope) is (ironically) melancholic; and Nurgle (god of despair and disease) is phlegmatic.
The final Hasse Och Tage revue Fröken Fleggmans mustasch is constructed around this trope, to the extent that the characters of the four person ensemble (if one excludes the pianist) are named accordingly. The quartet consists of:
In Mozart's opera Don Giovanni: Donna Elvira (choleric), Masetto (choleric/melancholic), Donna Anna (melancholic), Leporello (phlegmatic), Zerlina (sanguine), Ottavio (sanguine/choleric), and Commendatore/Don Pedro (leukine/phlegmatic).