“Kung Fu Panda,” the 2008 animated film from DreamWorks, was the kind of project that could have easily gone south. Its premise sounded like an overworked twist on “Dumbo” — if an elephant can fly, why can’t a panda become a martial artist? — and there didn’t seem much promise in such unspectacular sidekicks as Crane and Mantis. Casting Jack Black as the voice of Po, the title role, had potential for irritation.

Instead, “Kung Fu Panda” proved a winning combination of cuddly cuteness and kick-butt action, with the bonus of a tender relationship between Po and his adoptive father, a doting goose named Mr. Ping (James Hong). The sequel, in 2011, set a milestone, becoming one of the highest-grossing films directed by a woman. Jennifer Yuh Nelson returns to direct “Kung Fu Panda 3” (aided by Alessandro Carloni), continuing a winning streak for one of the best animated franchises currently running.

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In this entry, Po encounters two new figures: One is his long-lost father, Li (Bryan Cranston), a blustery adventurer who whisks Po away to a magical village full of his roly-poly brethren. The other is Kai, a yak-like villain with the rumbling voice of J.K. Simmons, who is stealing the chi of every Kung-Fu master in China. Things come to a head when Po realizes that the fate of his new home is in his hands.

Like its predecessors, “Kung Fu Panda 3” feels a little overstuffed. There are more themes — identity, family, responsibility — than one movie can handle. Supporting characters like Tigress (Angelina Jolie) and Viper (Lucy Liu) get short shrift as usual, although Dustin Hoffman’s long-suffering Master Shifu is still a delight and the serene tortoise Master Oogway (Randall Duk Kim) makes a welcome comeback.

As always, what makes this franchise work is the smart writing by Jonathan Aibel and Glenn Berger, who punctuate the action and slapstick with emotional chords (Li and Mr. Ping become Po’s nontraditional “dads”). The movie also looks marvelous, with an eye-catching blend of 2-D and 3-D animation and a finale that positively glows with light and color. Listen closely for cameos from Al Roker, Jean-Claude Van Damme and several young Jolie-Pitts.