The follow-up to 2011’s “The Muppets,” “Muppets Most Wanted” in fact begins just after  the prior film’s finale, as all the Muppets are standing around in the calm after the big finish wondering what, exactly, is next … and then breaking into a razzmatazz musical number, “We’re Having a Sequel …” It’s just the first of many meta-showbiz gags as Kermit, Piggy and the gang embark on a European tour with minor complications in the form of Constantine, a master criminal who — but for one mole — looks exactly like Kermit taking Kermit’s place to facilitate a series of heists. Then again, from their ragtag beginnings with their mock-variety TV show and up to the present day, the Muppets have never meta-showbiz gag they didn’t like …

Directed by James Bobin and written by Bobin and Nicholas Stoller, “Muppets Most Wanted” doesn’t have the presence of Jason Segel and Amy Adams, as was the case in “The Muppets,” nor is it quite as suffused with nostalgia. While new, point-of-view Muppet Walter (Peter Linz) is back, this time around the script and film don’t have to do the heavy lifting of getting the Muppets back onto the big screen after a 12-year absence in the wake of 1999’s “Muppets in Space” as the previous entry had to. (People who liked “The Muppets” for its heartfelt emotions and real core of feeling will like “Most Wanted” a lot;  people who hated “The Muppets” for focusing on Walter, Segel and Adams at the expense of much-loved characters will far prefer the new film as well.)

I am a fool for any film where a character has a signifying birthmark (see also “The Court Jester”), and the fact that Constantine is voiced not by Kermit puppeteer Steve Whitmire but instead Matt Vogel is a smart decision; it’s a tribute to the experience and skill of the Muppeteers that Constantine has entirely different body language than Kermit, right down to a wrinkled lip and sneer of cold command, despite having a body made of felt.  When Constantine takes Kermit’s place, of course, Kermit gets swapped in to his, sent to a Russian gulag commanded by Nadia (Tina Fey) ; while there’s some nice funny stuff (including Kermit organizing a prison talent show), it does remove him from the rest of the action as the Muppets play London, Madrid and Dublin to give Constantine and his second-in-command Dominic Badguy (Ricky Gervais, surprisingly funny) the chance to steal, with CIA agent Sam the Eagle and Interpol’s Jean-Pierre Napoleon (Ty Burr) giving the heists chase.

There are jokes that kids will get — when Kermit and Constantine face each other through a empty mirror frame, the bit is so funny you don’t have to know it owes a debt to the Brothers Marx. But there are also jokes just for you, like when two less-seen Muppets note how Walter’s arrival to the gang has upset what used to be the natural order, or how Jean-Pierre Napoleon’s coffee cups and cars are as small as his self-importance is colossal.  The songs are brightly and sprightlier, courtesy of Bret McKenzie, and the cameos here actually work far better — and much more organically — than they did the last time out, including a few very wicked gags at the willing expense of the participants.

If “The Muppets” was wistful — including its portrait of a Kermit who’s part Citizen Kane and part Carson post-retirement — it was so by design; getting the band back together was a fine enough plot. But “Most Wanted” has no such obligation to the past and neither ignores it nor wallows in it; it’s just another fun time with the gang, even if the scope and scale mean that some favorites (Pepe the Prawn, Lew Zeland) get short shrift. With a number of returning craftspeople — from cinematographer Don Burgess to editor James Thomas, costume designer Rahel Afiley to composer Christophe Beck — “Most Wanted” continues the new-school adventures of the Muppets with good humor, good intentions and strong filmmaking, and hopefully won’t be the last time we see this iteration of these characters on the big-screen.