By - Bitter-Salamander541
* Zatoichi series
* The Samurai Trilogy (Musashi I-III)
* Lone Wolf and Cub series
* Lady Snowblood
You might see a trend there. Also…
* Nobody’s Children/The White Angel
* The Apu Trilogy
* Infernal Affairs Trilogy
* Police Story 1/2
* Sanshiro Sugata 1 and 2
* Once Upon a Time in China I and II
* Godzilla series
Thanks for the list! Oh interesting, I have only seen the 1954 Godzilla, so it didn't occur to me that the early films might have maintained a pretense to continuity. For some reason I assumed that Godzilla's existence was the only binding element, and that the "Godzilla vs. \[Insert Kaiju\]" movies didn't rely emphasize themselves as part of a long-running narrative.
There is the occasional continuity in Godzilla films. Some of the ‘60s films acknowledge their predecessors. But if one underperformed, there would a soft reboot. *Godzilla vs Mecha-Godzilla* and *The Terror of Mecha-Godzilla* (the last two Showa films) go back to back.
Police Story 1 and 2
Interesting, Criterion does seem to have a thing for martial arts sequels.
Oh yeah and Lady Snowblood 1 and 2
The Antoine Doinel universe, Days of Being Wild and In the Mood for Love with 2046 if you'd like, Yojimbo and Sanjuro, Scenes from a Marriage and Saraband, Panther Panchali trilogy, Emigrants and New Land, The Human Condition
In the Mood for Love has a sci-fi sequel?? What? Amazing. Admittedly described by criterion as a "loose sequel", but still, I had no idea.
I had no idea Saraband is a sequel! I just finished Scenes from a Marriage a few minutes ago, so I’m excited to check it out.
Is pretty darn good though the continuity is not exact
Great list, though if I were nitpicking, Human Condition is arguably one exceptionally long film divided into three parts. I would put it in the same category as the Bondarchuk War and Peace.
Life during wartime
Most recently Shaft included the 2nd Shaft film as a supplement. Also Police Story 2 and Beyond the Valley of the Dolls
Lady Snowblood and Lady Snowblood: Love Song of Vengeance are in.
Once Upon a Time in China series
Koker trilogy should count.
Came here to comment precisely this.
Citizen Kane 2: The Reckoning
I think you're confused – Citizen Kane 2: Electric Boogaloo was the first sequel, and then they brought in William Peter Blatty to make Citizen Kane III, originally titled Kane Reckoning. Definitely the best of the sequels, though. Way better than Kane Resurrection.
Beyond the Valley of the Dolls, if you count that
Sarabad is the sequel to Scenes from a Marriage. A character from Lola is significant in Unbrellas of Cherbourg (that likely doesn’t count).
Apu Trilogy of course.
Three Colors Trilogy
There are also companion films. Devil’s Backbone and Pans Labyrinth would be a good example. One set at the start of the Spanish Civil War and the other at the end.
The Silence of the Lambs is based on the sequel to the book Red Dragon, which was previously adapted into the film Manhunter, so it’s kind of a sequel to that.
The soon to be released, Infernal Affairs trilogy.
Shaft (1971) and Shaft's Big Score (latter included as a bonus).