Ever since “This Is Us” became a surprise hit 3½ years ago, NBC has been searching for another show like it. A show about family. A show with heart. A show millions of viewers will watch.

And it’s possible that “Council of Dads” could be that show.

The pilot, which airs Tuesday at 9 p.m. on NBC/Ch. 5, isn’t great, but it’s very watchable. And it plays upon the emotions and tugs at the hearts of viewers. And maybe — just maybe — this is the kind of show that Americans trapped in their homes by the coronavirus will gravitate toward.

Just make sure you have the hankies ready to wipe away your tears.

Based on Bruce Feiler’s book “The Council of Dads: My Daughters, My Illness and the Men Who Could Be Me,” it’s about the Perry family — married couple Scott (Tom Everett Scott) and Robin (Sarah Wayne Callies) and their multiracial brood of both biological and adopted children. Scott is charming and funny and loves his wife and children a lot — but he’s been diagnosed with an aggressive form of cancer and he’s not long for this world.

The hourlong pilot jumps from fall to winter to spring to summer, and Scott does not make it to the end of the year.

(None of the other nine episodes in Season 1 cover more than a few weeks; some take place over just two to three days.)

Scott leaves behind letters to three of his best friends, recruiting them to be a “council of dads” to help raise his children. There’s Anthony (Clive Standen), Scott’s oldest friend. Oliver (J. August Richards), Robin’s best friend and fellow doctor. And Larry (Michael O’Neill), a gruff, older man Scott befriended at Alcoholics Anonymous.

(Photo courtesy of Evans Vestal Ward/NBCUniversal) Tony Phelan and Joan Rater are the executive producers of “Council of Dads.”

Executive producers/married couple Joan Rater and Tony Phelan — longtime writers/producers on “Grey’s Anatomy” — “kind of took this idea from Bruce Feiler’s book and grafted our own family onto it,” Phelan said. Feiler had two daughters, asked six men to be on his council, and survived his cancer.

Scott has four children when he’s diagnosed, he asks three men to be on his council, and he does not survive. And his children — Luly (Michele Weaver), Theo (Emjay Anthony), Charlotte (Thalia Tran) and JJ (Blue Chapman) — come in a range of ages and ethnicities, and reflect the Phelan/Rater family.

“Our daughter, Sally, we adopted from China,” Phelan said. “And our son, Tom, is transgender. ... If you put the four of us on our Christmas card, you wouldn’t necessarily say, ‘Oh, I get that family.’ But increasingly, I think that’s the way family looks in America today. And we were interested as parents in telling some of those stories that we lived through.”

“The show is very much in the present — this family moving forward from this very devastating event,” Rater said.

(Photo courtesy of Jeff Lipsky/NBC) “Council of Dads” stars Steven Silver as Evan Norris, Thalia Tran as Charlotte Perry, Michael O’Neill as Larry Mills, Michele Weaver as Luly Perry, Emjay Anthony as Theo Perry, Clive Standen as Anthony Lavelle, Sarah Wayne Callies as Robin Perry, J. August Richards as Dr. Oliver Post, Blue Chapman as JJ Perry.

Fact-based or not, the show’s greatest flaw is that it feels contrived. Diversity is great, it’s admirable, it’s absolutely what we should be seeing on TV. But this extended family includes Caucasian, Asian American, African American and mixed race members who are straight, gay and trans. And don’t forget the recovering alcoholics.

It feels like they were going down a list and checking boxes. Which may seem less glaring once viewers get a chance to really know these characters in upcoming episodes.

And this show has its heart in the right place.

“The message of it is so simple that it really hits me in a place where I live,” Richards said, “which is that family is really not limited to race, sexual orientation, not even genetics. Your capacity to love is what makes your family.”

I love that sentiment. And I hold out hope that I might — just might — fall in love with “Council of Dads.”

TRYING AGAIN • This is the second TV adaptation of Feiler’s book. Nine years ago, Fox spent big bucks on a half-hour comedy version of “The Council of Dads” — only to reject the show.

NBC has some history with this sort of thing. In 1990, it launched a sitcom adapted from the 1989 movie “Parenthood” — and it lasted just 12 episodes, despite the fact that Leonardo DiCaprio was a series regular.

Two decades later, NBC launched an hourlong drama adaptation of “Parenthood,” and it ran six seasons and 103 episodes.

WEIRD SCHEDULING • NBC will air the premiere of “Council of Dads” on Tuesday at 9 p.m., right after the season finale of “This Is Us.” And then you’ll have to wait more than a month to see the new series again.

“Council of Dads” moves to its regular time slot — Thursdays at 7 p.m. — on April 30.