Rotating Arcs

Rotating Arcs function like one of those revolving doors you invariably get your coat trapped in - as one character, or group of characters, come in, another is pushed out. While this can happen on a character-by-character basis, it's much more likely the the writer will make use of a Cast Herd.

Rotating arcs that employ cast herds need to do so in a fairly specific way in order to be successful. Outside of the main protagonist and his pals, the "pure" Cast Herd usually consists of a spokesman and several almost-faceless subordinates. However, a Rotating Arc with a cast that consists of one person with a personality and several clones is hardly going to hold the audience's attention, especially since the audience will be stuck with that particular group for an extended period of time. The solution is to focus on a certain, small (usually between 3-7 characters) subset of the cast, ignore all the other characters for the duration, and flesh out the smaller group's individual personalities and relationships to each other for the time it takes to complete a Story Arc. That time may be as short as one episode/issue, but is usually a run of several.

The rotating arc's cast herd is therefore unlikely to consist only of one "type" of character, since it could lead to an overdose of that particular type. For example, six eeyores are likely to become too apathetic to do anything by page 4, while six ditzes for an entire arc are likely to drive the viewer/reader to homicide. This type of Cast Herd is far more likely to be a smaller version of the main, large cast, with a relevant grouping of different personalities.

Once one arc, featuring one particular team, is finished, the writer ties up the loose ends and moves on to another set of characters. There may be a cross-over segment where the team that is finishing up passes on information to the team who's just getting started on their storyline, but then the former team will exit, stage right, until their turn comes around again.

There is an added bonus for the writers here in that when separate cast herds do form an alliance and appear together, it's a big event. If they've done the characterisation of the smaller groups well enough, readers are usually eager to see how they react to each other. "Like sodium and water" is usually the preferred answer for maximum drama, as various team leaders jostle for dominance, love interests suffer jealousy attacks, and deadpan snarkers unite to annoy the hell out of everyone. By the end of this chaos, even the most enthusiastic members of the audience may be a bit relieved to return to the usual one-team-at-a-time format, if only to catch their breath for a bit.

If a character changes groups, or the cast in its entirety is switched around, this is generally an arc in itself, as the fundamental ingredients of the book/comic/show have changed and new character dynamics have to be established.

It sounds a bit ruthless that one set has to kick out another in order to get their turn, but in actual fact this is probably the most popular way of handling Loads and Loads of Characters. It reduces two-dimensional characterisation, still employs Ensembles to appeal to the maximum number of readers, and decreases the number of occurences where one character is Out of Focus. Or at least placates the fans with the reassurance that their favourite hero will get a turn in the spotlight too. Eventually.

In effect, this is somewhat akin to writing several character-intense short stories and joining them together, rather than spreading yourself thin writing a long novel with far more characters than can realistically be handled.

The Rotating Arc isn't infallible though. Sometimes it seems that the revolving door has done a 360 degree spin, and the same characters turn up over and over again, at everyone else's expense. An individual character may take up residence in several groups, which is good in moderation as it provides the teams with a mediator (or, at the very least, provides more Wangst when there's a conflict of interests and they're stuck in the middle). Overuse it, though, and readers/viewers will likely get sick of the sight of him/her. There's also the risk that one Cast Herd will be significantly more appealing than the others, so to prevent this, personalities within the groups have to be balanced carefully.

Examples of Rotating Arcs include:

Anime and Manga

Ah! My Goddess does this on a smaller scale, with shorter arcs. Roughly, Keiichi and the goddesses form one troupe, the demons another, and the Nekomi Tech side characters a third.
Fruits Basket, in the manga's later arcs, as a necessity of parents, brothers, sisters, love interests and random passers by getting roped into the story. Notable for splitting up the core quartet of Yuki, Kyo, Shigure and Tohru. Kyo and Tohru form an arc unto themselves, Yuki begins to appear only in his own student-council related arc, and Shigure only really has any significance when shown with Akito. And let's not get started on the lives and loves of the other members of the Zodiac, who keep the Rotating Arcs spinning around at warp speed.
Naruto filler arcs typically follow this pattern. With Sasuke having left the village and Sakura spending all her time training under Tsunade, Naruto typically goes on a mission with other squads, usually with a different character getting emphasis and development in the arc. For example, in the Mizuki Strikes Back arc, he works with Team 10 and Iruka and Mizuki's past is explored; in the Bikochuu arc, he goes with Team 8 and Hinata's growth as a ninja is explored. In some arcs, like Land of the Sea, the featured characters come from multiple teams. Shippuden follows this to some degree with its arcs (Team Guy in the Gaara arc, Team 10 in the Hidan and Kakuzu arc, and Team 8 in the Hunt for Uchiha arc).
Upon the conclusion of the Johto arc, the Hoenn arc introduces Pokémon Contests into the Pokémon anime and a main character to participate in it (May, and later Dawn in the Sinnoh arc), giving it as much importance to the plot as that of Ash's story. This way, Hoenn suffered from less Filler than Johto (which was infamous for large amounts of filler), giving it much better reception. The following Sinnoh arc, unfortunately, didn't follow suit.

Comic Books

The X-Men uses rotating arcs constantly - with such an enormous cast, and people leaving, dying and resurrecting themselves all the time, it's the only way Professor X and Co. can be kept in check... and the only way that readers can keep up with everyone. Even then, the X-Men shuffle teams pretty regularly, just to keep things confusing.
Noticeably averted in Stormwatch and The Authority, where the teams are really too small to divide everyone up.
- Stormwatch does a Lampshade Hanging on this in "Bleed", where, after viewing a parallel world where there are several Stormwatch teams, Winter remarks "You can't put twenty superhumans in the same town without them picking fights with each another."
  - It can be argued, though, that these comics do a mini rotating arc within the issue by pairing up some of the characters: for example, in The Authority, Midnighter and Apollo, and Jack and The Engineer usually work together as well as being romantically linked while Shen and The Doctor alternate between teams/partners or work alone. Oh, and Jenny (both versions) does whatever the hell she likes.

Literature

Steven Erikson's Malazan Book of the Fallen series fits this. Every book has a huge cast of characters and lots of different yet strangely interrelated plots.
- The books began as a relatively tight collection, with one or two plots per book, then, as it went into the middle books of the series, expanded to have a huge cast of characters, all involved in dramatically different plots, at different scales of power, at different times, with very slight connections between them. As the end approaches, those connections are becoming more obvious, and there may even be a wrapping up of loose ends.
Discworld does this. Each book's main group is traditionally either Ridcully and the Wizards, the Witches and Tiffany Aching, Death/Susan, the Night Watch, Moist Von Lipwig, or a stand-alone book who's characters aren't visited again outside of cameos.
To a lesser extent, The Lord of the Rings, particularly The Return of the King—the cast herds are Frodo-Sam-Gollum, Aragorn-Eomer-Imrahil, and arguably two or three crystallize around Eowyn and Faramir. They all occur simultaneously but in multi-chapter segments.
George R.R. Martin has started to do this with ENTIRE BOOKS comprising one "arc" in his A Song of Ice and Fire series. A Feast for Crows, only followed about half of the cast, while Dance with Dragons focused on the other half. The casts came together for the last third of the book. Also, the first three books heavily focused on Stark family protagonists (in the first book, 6 out of 8 of the main viewpoint characters were from that family). Subsequent book have shifted focus to other families while the surviving Starks for the most part hide and regroup.
The Redwall books are organized like this generally. There's usually 1-3 groups off on the adventure and 1-2 groups dealing with some issue that arises back home while they are gone. At least one Villain group (depending on the number of lead villains) is usually present as well, but they also tend to get less personal attention beyond their actions relevant to the adventurers.
The Valley of Horses rotates between Ayla and her pets and Jondolar and his brother.

Live-Action TV

This is a staple of the Law and Order franchise, and is especially prevalent in the main show and Criminal Intent. Depending on actor availability or shooting needs, any given season can flip back and forth between two separate sets of detectives investigating cases at different times, or overlapping casts during a crossover event.
The Bill. Not only do we have CID, Uniform and The Brass, but several sets of external characters. These can be left hanging for months before being rotated back in, putting a strain on viewer engagement.
In its last two seasons of The West Wing, the plot went back and forth between the White House and the campaign trail, but most of the Story Arc revolved around the upcoming election. Since the candidates had to comment and respond to the crises the President dealt with and the campaigners were still in touch with the characters remaining in the White House, there was a degree of overlap.

Web Comics

Friendly Hostility characters can be grouped roughly into "Fox's friends" and "Collin's friends," and tend to appear as such, one group at a time. There's quite a bit of overlap though, and this is one particular comic that likes to see what happens when the separate cast herds meet.
Gunnerkrigg Court uses Rotating Arcs, even though the cast isn't particularly large. Characters and plot threads come and go from chapter to chapter; Antimony is the only constant, and even she gets demoted to the role of a spectator in a few chapters.
Sluggy Freelance does this a lot. Bun-Bun got his own story arcs and cast of supporting characters in "Holiday Wars" and "Oceans Unmoving." Same goes for Oasis in "Phoenix Rising." Torg has had a number of these, from the "Torg Potter" stories where he's magically transported to a corner of the Sluggy universe populated by Harry Potter parodies, to the "Aylee" arc where he and Aylee were trapped for months in Another Dimension, to the massive "That Which Redeems" arc where he was in Another Another Dimension for months without any of the other cast members (although he did have their Alternate Universe versions). The other main characters have all gotten smaller versions of these, usually in shorter arcs with a little more interaction from the other cast members.
The webcomic Schlock Mercenary does this in the "Massively Parallel" Story Arc. The mercenaries of Tagon's Toughs split into four teams while their wrecked ship was in drydock. The first arc covered Elf Foxworthy's struggle to get the ship fixed, while the megalomaniacal Fleetmind pursued its own suspicious goals behind the scenes. The second arc has Schlock and his team sent on a mission that is going toxic. Pieces from the first arc keep getting shown from the other side of the comm system. The third arc has Kevyn and Pi setting up a system of explosives and teraports for an emergency escape system (the requested work, if not what was actually planned).
El Goonish Shive switches to this form and back, as much as possible with one main team in two schools. More distinctive in "Night Out" (Martial Arts Crew, Elliot's Crew, Ellen's Crew) and recent arcs (the first half of Hidden Genesis: MIB; second half, and the second half of "Sister II": Nanase, Ellen, Grace; "Hammerchlorians": Susan, Sarah, Grace) where out-of-limelight cast is mostly absent. In others the different subsets of both main and support characters get a spotlight, but the rest still maintains at least token presence.
The Meek makes full use of this, seeing as it has three different protagonists in different parts of the world, which each chapter focusing on a new character dealing with the story. The first arc deals with Angora, a green-haired, Green Thumbed Innocent Fanservice Girl who is to decide the fate of the world (and is arguably the "main" character). The Second follows Luca, the emperor of Dia' most powerful country, and the third follows a bounty hunter named Soli. The fourth chapter returns us to Angora.
The Order of the Stick uses this to an extent, with a minimum of a dozen strips at a time focusing on the Order itself or one of their enemy groups. However, this trope is most apparent during the Don't Split the Party arc, where (as the name implies) the Order is split, following the conclusion of the previous arc—there's Roy hanging out in the afterlife; Haley and Belkar leading La Résistance in Azure City, before leaving with Celia to try and resurrect Roy; Durkon, Vaarsuvius, and Elan in the refugee fleet dealing with Daimyo Kubota's scheming; and on top of that, there's Team Evil solidifying their hold on Azure City.
Homestuck starts out moving between its separate protagonists, and gets even more and larger groups as time goes on.

Web Original

The Whateley Universe has to operate this way, since the main characters are written by different authors. The most obvious example was the 2006 Christmas break, which technically still hasn't finished since some authors are writing new stories for it. Phase had a separate novel where she went home and ran into a serial killer that was really an unkillable demon from a hell dimension. Tennyo had a Christmas adventure with Jinn Sinclair who was embedded in her stuffed cabbit, while Jade Sinclair went home with Fey for another holiday and she was stabbed to death, but she got better. And so on. So far, there are seven such stories, two of which haven't finished. And Word of God says there will probably be a couple more.