A reliance on guest stars and gimmicks often means a popular TV series has “jumped the shark” — a way of saying the show’s writers and directors have exhausted themselves creatively. The funny thing about “Only Murders in the Building,” the Emmy-nominated comedy series about mysterious deaths at a New York apartment residence, is that right from the start, the show frequently featured daft tangents and guest stars as disparate as Sting, Nathan Lane, and Tina Fey. 

Its second season continued the occasional inanity and stunt casting with appearances by Amy Schumer, Shirley MacLaine, Mark Consuelos, and model Cara Delevingne, among others. Last year’s third season then upped the absurdity ante considerably by having most of the plot revolve around the production of a Broadway show, with Meryl Streep, Matthew Broderick, Paul Rudd, and others hamming it up, to more or less amusing effect. 

For its fourth season, having its premiere this week on Hulu, the show once again flies in the face of potential criticism and viewer exhaustion by weaving the making of a Hollywood movie into its plot, with guest stars galore. Happily, based on the first three new episodes, the series is still in fine, funny form, despite the arch meta-narrative and many big-name appearances. 

It could even be said that the “inside Hollywood” angle of the latest season has energized the writers and directors, with the jokes sharper and comic set pieces zanier than the third season’s often belabored theater-geek references and stage clichés, notwithstanding some great original songs.   

The return of the three appealing lead actors is certainly welcome: Steve Martin as an insecure former television actor, Charles-Haden Savage; Martin Short as a flailing Broadway director, Oliver Putnam; and Selena Gomez as a taciturn millennial drifter, Mabel Mora. After last season’s cliffhanger — essentially, “Who shot Sazz Pataki?” — the new season begins with our heroes unaware of the murder of Charles’s friend and former stunt double. Oliver’s Broadway musical has been shuttered, but soon he and his cohorts are flying to Los Angeles to meet with Paramount executives to discuss a movie inspired by their popular “Only Murders in the Building” podcast. 

Once at Paramount Studios, they realize a film doesn’t need to be pitched so much as signed off on, as it’s practically in pre-production — with a writer, director team, cast, and release date already in place. At a swank Hollywood party, the three meet the famous actors who are to portray them: Eugene Levy will play Charles, Zach Galifianakis is Oliver, and Eva Longoria is Mabel. Roll camera on awkward, almost-existential scenes between the main characters and their “actorly” counterparts.

Having the plot partly revolve around the production of a movie dovetails nicely with Oliver’s relationship with Loretta (Ms. Streep), who is now in L.A. working on a hospital series, and with the fact that the missing Sazz was a still-working stunt woman. (The joke that Sazz — played by the tall and proudly lesbian Jane Lynch — often doubled for male actors like Martin’s character and the real Scott Bakula continues to pay dividends.) Homages to stunt actors, references to and clips of movies like “Once Upon a Time in the West,” and digs at the industry all combine to create a mix of reverence and irreverence toward Hollywood.

By the end of the first episode, though, the threesome are back at the Arconia, their Upper West Side apartment building that, considering it’s the incongruous site of so many murders, should have police tape permanently surrounding it. There they find the remains of Sazz in the property’s basement incinerator, and before you can say “how convenient,” our budding sleuths/podcasters are on the hunt for the killer, who clearly intended to murder Charles instead. 

Feeling guilty over Sazz’s death, Charles starts seeing and speaking to his friend in his mind, and this affords an opportunity for Ms. Lynch to continue to deliver quips and asides in her trademark breezy but pungent style, not to mention having Mr. Martin be humorously frazzled. 

More guest stars are introduced, including Kumail Nanjiani and Richard Kind, and though one can see right through their red herring characterizations, there’s still great fun to be had, particularly in the third episode when our individual protagonists are joined by their respective thespians for a trio of comic set pieces. These back-to-back-to-back scenes, one of which involves the theme song to the sitcom “Perfect Strangers,” may prove to be one of the highlights of the season.

Not every bit of comedic business lands in these first three episodes, but each one contains a high percentage of clever lines and hilarious scenarios. The season’s Hollywood theme, amusing self-awareness, and compelling murder case already distinguishes it, though whether forthcoming episodes will include one as brilliant as the first season’s dialogue-less “The Boy from 6B” remains to be seen. 

Having “jumped the shark” a while ago and yet maintained popularity and praise, the creatives and cast of “Only Murders in the Building” don’t have to worry about strict logic, reality, and artistic integrity — only lite mystery and looniness.