http://tvtropes.org/pmwiki/pmwiki.php/Main/Interquel

The sequel just got PREQUELIER!

Timon: Waaaait, wait wait wait, hold on a second. Three? What's with the three? No, no, no, the three has got to go.

Pumba: Timon, you can't use Two! There's already been a Two!

Timon: Mmm, you've got a point there, big fella. It's not a sequel, anyway.

Pumba: Yeah, more like a Behind-the-scene-quel!

Timon: A what-a-who-quel?

Pumba: Oh, you know, an Inbetween-quel! The Lion King 1½; teaser note The ironic fact being that some countries saw the release of the film with the 3 still on the end. Waaaait, wait wait wait, hold on a second. Three? What's with the three? No, no, no, the three has got to go.Timon, you can't use Two! There's already been a Two!Mmm, you've got a point there, big fella. It's not a sequel, anyway.Yeah, more like a Behind-the-scene-quel!A what-a-who-quel?Oh, you know, an Inbetween-quel!

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Also called a Midquel, this can be one of two things: when a new entry in a series is a sequel to one existing entry, and a prequel to another, or when it takes place during a Time Skip in an earlier entry rather than continuing the story. This device is often used to expand a portion of the story only touched upon in other entries, or if more story is desired but there's no logical place for it either before the beginning or after the end.

The two terms are sometimes differentiated, where an "Interquel" is referred to as an entry happening strictly between two previous ones of the franchise (i.e. Movie 3 takes place between Movie 1 and 2), while a "Midquel" takes place within a single work of the franchise (i.e. Movie 2 takes place within a Time Skip in 1). But continuity can sometimes be so convoluted (depending of whether it is an Immediate Sequel or not, or whether The Stinger overlaps with events from the other works), that establishing a work is in-between two others will usually suffice.

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Compare Prequel, P.O.V. Sequel. Not to be confused with Simultaneous Arcs which is a story that takes place at the same time as another story, but focusing on different characters.

Examples:

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Anime and Manga

Audio Plays

Big Finish Doctor Who: Every Big Finish audio drama featuring the Doctor takes place between television stories during the relevant incarnation's run. In several cases, they are set during a television story: All of the stories in the Companion Chronicles and the Early Adventures featuring the First Doctor, Steven Taylor and Sara Kingdom take place during "The Daleks' Master Plan", specifically between the seventh episode "The Feast of Steven" and the eighth "Volcano". In "Excelis Dawns", the Fifth Doctor and the unseen Tegan Jovanka arrive in Excelis on the planet Artaris after they drop off the Gravis on Kolkokron in the fourth episode of "Frontios" and before they return to the titular planet for Vislor Turlough later in the same episode. "Winter", the fourth story in the anthology "Circular Time", takes place during the Fifth Doctor's regeneration in "The Caves of Androzani". "Return of the Daleks" takes place between the second and third Dalek Empire stories, "The Human Factor" and "Death to the Daleks!".



Comic Books

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Fanfiction

Film  Animated

Film  Live-Action

Literature

Live-Action TV

Multiple Media

Radio

Torchwood: The Lost Files was set between series 2 of Torchwood and the miniseries Children of Earth except the last one since the team ceases to exist at the end of Children of Earth and wasn't reformed until Torchwood: Miracle Day Ianto can be in it .

Theatre

The stunning, lightning-fast plot of The Progeny take place in between Sophocles's first two Oedipus plays and his first play, Antigone.

Video Games

Visual Novels

Webcomics

Nebula has "Nix", a short story from Pluto's perspective. It takes places at some point between #10 (Black Hole first contacting Pluto) and #14 (Black Hole finally making her move).

Web Original

The Dreamer has short stories that can be read as these and as A Day in the Limelight stories.

Western Animation