Earlier this summer "Toy Story 4" premiered to rave reviews and financial success. It disproved the naysayers (myself included) that thought it was going to be bad or pointless because it felt like an unnecessary sequel after the third film felt so "final". This lead me to question why most film series restrict themselves to only three entries.
This statement isn't completely true. Some film series like Marvel, Star Wars, and Harry Potter obviously have more that three entries. However trilogies are still present even within these franchises. Marvel has a trilogy of Iron Man, Captain America, and Thor (for now) films. Star Wars' "Skywalker Saga" is even made up of a trilogy of trilogies (the original trilogy, the prequel trilogy, and the sequel trilogy). So why are three films in a series standard.
This standard mostly has it's roots in the standard of narrative writing itself. Most stories typically have a beginning, middle, and end. Most film series are viewed through the lens of one massive story line (The Lord of the Rings trilogy comes to mind), so it makes sense that they follow that narrative structure. The first film often acts as the introduction, setting up characters and the main plot.
The second film acts as the middle of a story where characters are examined more closely and the driving plot thickens with plot twists or deeper meaning added to it. The third film acts as a finally to the story, wrapping everything up in a nice little bow and concluding our characters' arcs. Trilogies are often used if you want to make a film franchise, but still want to tell a complete story from beginning to end.
This is where you often see a difference in the amount of films made for a series. Many film series that go over three entries don't have an overarching plot and are more serialized, self-contained films, such as the James Bond films, the Mad Max films, the Alien films, or the Transformer films. On rare occasion, you have a series with an overarching narrative that needs more than three entries to tell it (the John Wick films immediately come to mind).
The number of films in a given franchise is often limited to how many the creator feels are needed to tell a full story, which is often why three is the magic number. Many franchises that go beyond three entries tend to be viewed as desperate for money or an unnecessary film milking a franchise to death (which is what many thought "Toy Story 4" was before it came out). However, I feel stories should not be restricted to a set number of films to tell a story. If a film makers feels like they can tell a story in 2 films or 12 they should do it. After all the Marvel Cinematic Universe just wrapped up a compelling story line in "Avengers: Endgame" and they told that story over 22 various films in a little over a decade's worth of time.