There are busy stage directors, and then there is Kenny Leon. After helming 11 Broadway productions between 2004 and 2020 — among them two revivals of “A Raisin in the Sun,” the latter of which starred Denzel Washington and earned the director a Tony Award — Mr. Leon is only adding to his roster.

Just weeks after his production of Suzan-Lori Parks’s Pulitzer Prize winner “Topdog/Underdog” opened to glowing notices, previews began last Friday for Mr. Leon’s latest project: the Broadway bow of 91-year-old playwright Adrienne Kennedy’s “Ohio State Murders,” set to open December 8.

Also in December, Mr. Leon — who’s also making his debut as a Broadway co-producer this season, with a musical adaptation of the film classic “Some Like It Hot” — will launch a national tour of “A Soldier’s Play,” which earned him a Tony nomination two years ago. In May, he’ll direct a new play, Rajiv Joseph’s “King James,” off-Broadway.

“And I have another big project coming up in New York, not on Broadway, but I can’t talk about that yet,” Mr. Leon says. Nor can he spill details about the two Broadway productions he already has on tap for next season.

There is, the director notes, always a pattern and a purpose in his choices. “Topdog” and “Ohio State,” for instance, “are both by award-winning Black women who don’t have their plays on all the stages they should be on. And I think both plays look at Americans trying to find the true meaning of America, and what gets in the way. One happens to have two Black men exploring that, while with the other it’s a Black woman.”

Mr. Leon’s involvement in “Topdog,” a tragicomedy focused on two rivalrous but interdependent brothers, began when he and Ms. Parks “realized we had known each other for 25 or 30 years but hadn’t worked together. I felt this is the play the world needs right now, after Covid — two and a half years of being disconnected from each other — because it’s about our need to love on humanity more. And after the murders of George Floyd and Brianna Taylor, what better lens to look at that through than those of two Black American men, written by a Black American woman?”

The director stresses, “My point of departure for the play was, let’s start with the joy and the laughter, until we can’t [sustain it]. And Suzan-Lori really gave us the space to create something joyous and loving.”

“Ohio State,” which was written more than 30 years ago, appeared on Mr. Leon’s radar during the pandemic, when the producer Jeffrey Richards recruited him for a virtual presentation of the play starring a six-time Tony winner, Audra McDonald — whom Mr. Leon had directed in his first revival of “Raisin,” and later in episodes of television series such as “Private Practice.”

Mr. Leon had become acquainted with Ms. Kennedy’s work while still in college, reading “The Owl Answers” and her Obie Award-winning “Funnyhouse of a Negro.” “I said to Ms. Kennedy, ‘Your play needs to be on the highest stage.’ And she said, ‘That’s what I’ve wanted since I was 15 years old, and I’ve never had a play on Broadway.’”

Ms. McDonald, along with Mr. Richards, signed on for the Broadway premiere, in which she plays a writer based partly on Ms. Kennedy — herself an alumna of Ohio State — who encounters racism within the confines of academia. “The character is probably 50 percent Ms. Kennedy and 50 percent fictional: She won’t tell you where she draws the line,” Mr. Leon muses. 

The veteran playwright has nonetheless played an active role during the rehearsal process, Mr. Leon reports: “She sends me eight emails every day, and probably talks to Audra every other day. She sends me emails from her past, emails on her thoughts about certain parts of the play. Then I ask her questions and she hits me back with answers. It’s a good time.”

Mr. Leon’s own concerns about social justice have also informed offstage endeavors. He and Ms. McDonald are among the founding members of Black Theatre United, which since 2020 has promoted education and activism throughout the industry. “We’ve got to make it better for those coming up behind us,” he says. “Part of that is making sure that Black people have access to everything that comes with being involved in theater, especially Broadway theater.”

The organization’s first goal was to confront what Mr. Leon describes as “low-hanging fruit. Like, how about no all-white creative teams? And we got the unions and the theater owners to say, ‘You know what? The least we can do is have diverse creative teams.’ And the industry decided there’s no reason we can’t have a few theaters named after people of color, so we got the Lena Horne and the James Earl Jones,” the latter being home to “Ohio State.”

Diversity plays a predictably key role in the other artistic pursuits Mr. Leon is juggling in whatever spare time he has these days. He recently workshopped a revival of Melvin Van Peebles’s 1971 musical “Ain’t Supposed to Die A Natural Death,” and is also trying to find a theater for a new musical adaptation of the Eddie Murphy/Dan Aykroyd hit “Trading Places,” which had its premiere last spring at Atlanta, with a female actor playing a woman based on Mr. Murphy’s character.

“Maybe what we all need is to spend five minutes in each other’s shoes,” Mr. Leon proposes. “I just keep looking for projects that I think give us an idea of what a better world it could be if we could lean into the love, and try to listen to other folks, and have them listen to us.”