If the sweet, animated 2016 film “The Secret Life of Pets” was mostly for kids, its new sequel might be for another segment of the audience altogether — whoever is buying the tickets. Amid the cute critter shenanigans, this one has plenty of lessons for the parents.

Most of the same gang is back this time: Kevin Hart as the fluffy white bunny Snowball, Eric Stonestreet as the goofy giant Newfoundland, Lake Bell as the laconic cat Chloe and Jenny Slate as the plucky Pomeranian Gidget. This time, though, our main hero terrier Max is voiced by Patton Oswalt, replacing Louis CK who was removed after allegations of sexual harassment.

Both films in the franchise deal with a new addition to the family. In the first, it was a new dog that allowed the filmmakers to explore sibling rivalry. This time, the stranger is a baby, who Max learns to love unconditionally, but the infant also ups his anxiety levels. (Any helicoptering parent out there knows what we mean.)

Returning screenwriter Brian Lynch and returning director Chris Renaud, who also voices the guinea pig Norman, have actually concocted three interlocking plots in “The Secret Life of Pets 2.” It’s a wise decision since none are deep enough to carry the film alone, forcing some convoluted stitching together. But they manage it, creating a solid piece of entertainment for all ages, if not a terribly revelatory one.

In one story, Max finds himself ever fearful for his owner’s new toddler, stressing out as the boy’s protector. “Was the world always this dangerous?” he asks after a harrowing New York City stroll. He even develops a nervous scratching tick that requires a mortifying dog cone. A trip to a farm in the country seems to offer a respite. Getting his head right is his quest.

Before he leaves, he asks Gidget to take care of his favorite squeaky toy. She promptly loses it in a cat lady’s apartment filled with crazed felines. Getting it back is her comedic quest. Meanwhile, Snowball is asked by a brave Shih Tzu (newcomer Tiffany Haddish) to rescue a tiger cub held by a malevolent circus boss. His quest is, like the others ones, to find his inner superhero.

Oswalt is a fine replacement for Max, able to connect with the character’s timidity, wonder and blossoming courage. He is helped by a gruff farm dog voiced by Harrison Ford, who unfortunately muddies his first animated voice role with some hypermasculinity.

Ford’s alpha dog is pure action cool, ripping off Max’s cone in disgust (not the best message for kids in treatment), rejecting Max’s embarrassed neurosis and being the cold, silent type.

“The first step in not being afraid, is acting like you’re not afraid,” he advises.

Ford gets to play with his own he-man screen persona, but we’re not sure this John Wayne bit — or the whole dynamic of pampered city folks vs. tough country folks — is what we need right now. Another drawback is the scary elements: fearful wolves and an awful villain with a whip and a cattle prod.

Even so, the majority of the film is carefully constructed, switching from plot to plot to plot while also incorporating old characters — Dana Carvey’s elderly Basset hound and Hannibal Buress as dachshund Buddy — in an increasingly complex patchwork, fed by a lively soundtrack that includes Stevie Wonder, Jefferson Airplane, Coolio and ZZ Top.

As signs of how well- engineered this movie is, a cover of Bill Withers’ “Lovely Day” is used at the end, a callback to the original song’s appearance in the first film. It also opens with “Empire State of Mind,” an echo of how the first one opened with Taylor Swift’s “Welcome to New York.”

There are some nifty touches, including a dream sequence in which Snowball fantasizes about being a caped crusader, which creates a comic book sequence inside the animated film. Bell pretty much steals the movie when her cat gets high on catnip and later teaches Gidget the “way of the cat” — complete with mandatory walking on a laptop keyboard and batting mugs off tables. All this with extraordinary animated effects. You will marvel at how real the illustrators have made this world, from rocky cliffs to speeding cars and dazzling eyes. In a neat twist, too, the cat lady becomes the butt of jokes but also this — a heroine.

It all builds to a climax where all three plots converge, some stretched uncomfortably. Max is clearly the emotional center of the film but Snowball’s journey is just weird, starting as a bunny who plays a dress-up superhero, morphing into a real superhero who is revealed to be anything but before proving he is a superhero, kind of.

(Stick around at the end credits for a clip of Hart as a gangsta Snowball rapping “Panda” by Desiigner.)

If the knock on “The Secret Life of Pets” was that it was a rip-off of “Toy Story,” then the second film better grounds itself in its own universe. Like its main three characters, it has learned to be comfortable in its own animated skin.

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