Miss Piggy, Kermit the Frog and the rest of their stuffed gang of entertainers take their talents to Europe for the cameo-filled sequel “Muppets Most Wanted.” (Jay Maidment/AP)

When “The Muppets” came out in 2011, it was the first Muppet movie to hit theaters in more than a decade; the collective exhale was palpable — and profitable — as millions of relieved fans flocked to see their beloved yarn-and-wire characters mix it up with Jason Segel and Amy Adams in what amounted to Muppets 2.0. The film was such an unexpected smash that it earned Jim Henson’s creations their very first Oscar (well, not counting the Grouch) for the brilliant song “Man or Muppet.”

Muppets Most Wanted” can’t rebottle that particular brand of lightning, but it does a terrific job trying, and once again “Man or Muppet” songwriter Bret McKenzie — one half of the comic musical comedy duo Flight of the Conchords — saves the day with a passel of catchy and amusing ditties that keep the movie humming along even when the plot threatens to sag.

Written and directed by “Muppets” filmmaker James Bobin, with an assist from co-screenwriter Nicholas Stoller, the story picks up where “The Muppets” ended, with the troupe back together and contemplating their professional future. Enter would-be road manager Dominic Badguy (Ricky Gervais), who pronounces his last name “BAHD-jee” and lavishes the Muppets with promises of sold-out continental venues and stardom while a suspicious Kermit reluctantly goes along.

It turns out that the European tour that Badguy has arranged dovetails diabolically with a plan he’s hatched with an evil green Russian frog named Constantine, who could be Kermit’s double save for a menacing brown mole on his lip. Mistaken identities and high jinks — on stage and off — ensue. The Muppets take Berlin; Badguy and Constantine smash-and-grab their way from Madrid to Dublin to London; and Kermit languishes in a Siberian prison camp, befriending convicts played by Ray Liotta and Danny Trejo and winning the heart of a soulful guard named Nadya (Tina Fey).

If those marquee names get your attention, just wait: “Muppets Most Wanted” is stuffed to its felted gills with notable supporting and cameo performances, including a very funny turn by “Modern Family’s” Ty Burrell as a Clouseauvian Interpol agent. The one discordant note comes by way of the gulag gags: With Russian President Vladi­mir Putin enthusiastically reviving that country’s most oppressive totalitarian past, making light of what now seems all too real may strike adult viewers as, if not tasteless, then at least unfortunately timed. (The backfire also serves as a cautionary reminder to studio executives eager to exploit the newly all-powerful international market.)

Even with those misgivings, no one old enough to remember “A Chorus Line” will be immune to a set piece revolving around a prison theater revue; like most of “Muppets Most Wanted,” the wittiest jokes and cameo appearances are designed to soar far over the heads of young filmgoers and into the atavistic pop consciousness of their adult companions. As for the youngsters, it’s up to individual parents to decide whether the sight of Kermit being wheeled into jail trussed up like Hannibal Lecter is a tad too dark for Junior’s delicate sensibilities, or whether their littlest charges will truly appreciate an opening production number that invokes Busby Berkeley and Ingmar Bergman in addition to the Muppets’ own cherished oeuvre.

The title of that song, by the way, is “We’re Doing a Sequel,” a clever Hollywood sendup that firmly establishes the film’s governing tone of sly, self-referential irony. Gervais and Fey turn out to be the ideal human foils for that enterprise, playing along with game professionalism and never letting the audience see them wink (at least not too obviously). Kermit, Miss Piggy and the rest of the gang may pick up life lessons about the dangers of getting everything you want, the value of loyalty and the importance of listening to your gut, but their grown-up chaperones will simply be grooving on the songs, inside jokes and zestfully calibrated mayhem. In perhaps the toughest test of all, “Muppets Most Wanted” figures out how to end on a genuinely hilarious note — or, in this case, lack of one. Well played, Muppets 2.0. Well played.

★ ★ ★

PG. At area theaters. Contains some mild action. 112 minutes.