The first comes from The House Next Door (who else?), which posits that each Muppet film essentially is a new production from a troupe of actors:
It occurred to me that the Muppets—as defiantly modernist as any children's entertainment (dig the fake film-burn midway through The Muppet Movie, which caused the projectionist at the theater I used to program to freak out mid-screening)—are also an update of one of the hoariest and oldest theatrical traditions: a Commedia dell'arte troupe. Establish Kermit and Miss Piggy as The Lovers (their love plot serves as a major narrative thread in nearly every Muppet movie, including this one) and the rest of the troupe falls into place: Gonzo as the deformed, foolish Pulcinella; Rowlf as the self-effacing, loyal Pedrolino; Fozzie as Arlecchino, the slow-witted clown. The Muppet films speak to us in part because they reapply centuries-tested comic traditions to addressing and critiquing television and film themselves. Part of Jim Henson's creative genius was that he understood how to walk that delicate line between traditional storytelling and self-conscious address, and The Muppets Take Manhattan is a thorough application of his style. There is no narrative continuity between The Muppets, The Muppet Movie, and The Muppets Take Manhattan, and it's the creators' strong ability to create dynamic characters that allows them this freedom.The other theory is my own, and it's one which strives to integrate continuity into the film universe. Much as The Muppet Movie is a movie-within-a-movie about how the Muppets received The Standard Rich & Famous Contract and became stars (including towards its end the newly-famous Muppets filming an origins film), The Muppets Take Manhattan, The Great Muppet Caper and all the other Muppet films should be seen as the other films the now-famous Muppet actors are making within the universe of the first film. In other words, the first film is a story about the "real" Muppets becoming actors, and the rest are the films those actors have made -- with Fozzie Bear playing a character named "Fozzie Bear," etc. It explains, for example, how the "Kermit" and "Miss Piggy" characters can marry (in a musical within a movie, but for "real") at the end of Manhattan yet this marriage isn't acknowledged in subsequent films. These are the movies which Lew Lord of Worldwide Pictures signed them to make.
To be sure, Caper makes an explicit wink in this direction -- Kermit talks at the start of the film about the reporter roles that "Kermit," "Fozzie" and "Gonzo" are playing, but does so without tying himself to the prior narrative. Why not extend this all the way throughout the films? Isn't "The Muppet Show" just the variety show that these actors produce on their off days? Or, as usual, is this just a part of my brain which should have been more profitably devoted towards learning ERISA law?