Confessor. Feminist. Adult.

Near the end of his interview with Bill Murray, Howard Stern turned an already somber discussion about missed career opportunities into an existential grilling.

“Is there something that you question in your own life,” Stern asked, “like why haven’t I found that great love of my life?”

Murray audibly exhaled and let a pensive moment of silence pass. “Well, I think about that, I do think about that, that um, you know. I’m not sure what my — what I’m getting done here,” he said, sounding like a man questioning his ultimate purpose. Dating seemed like a bad idea, he went on, given that he was such a mystery to himself, and a mystery that he was not very eager to solve.

“What has stopped you from getting in touch with you?” asked Robin Quivers, Stern’s longtime co-host.

“What stops us from looking at ourselves and seeing ourselves is that we’re kind of ugly if we really, if we look really hard,” replied Murray, a part-time resident of Charleston. “We’re not who we think we are. We’re not, uh we’re not as wonderful as we think we are.”

As an irregular listener of “The Howard Stern Show,” I found this conversation, which took place in 2014, a bit startling. For years, Stern was known principally for pushing the limits of taste as the ringmaster of a raunchy circus of pranksters, oddballs and strippers. During his decades on terrestrial radio, his main passions seemed to be, in no particular order, boob jobs, prostitutes, lesbians and flatulence. Introspection and empathy were not fortes.

What I didn’t appreciate, until hearing Murray lay bare his deepest anxieties, is that since settling in to his new home on satellite radio, which he did in 2006, Stern and his show have gradually taken on an improbable new dimension. Scattered among the gleefully vulgar mainstays are now long, starkly intimate live exchanges, character excavations that have made Stern one of the most deft and engrossing celebrity interviewers in the business and a sought-after stop for stars selling a movie or setting the record straight.

“He’s truth serum,” said comedian Amy Schumer, who has been on the show four times in the last five years. “It’s like you’re under contract to be totally honest in there, and even though it’s being broadcast, it feels super intimate and protected, even though you definitely aren’t.”

By all accounts, the metamorphosis has been slow, the result of a combination of therapy, his second marriage, mainstream acceptance and a sixth sense Stern has about how to evolve with the times.

“I couldn’t have done the show I’m doing now 20 years ago,” Stern said over the phone. “I’ve changed a lot. I’d be sort of pathetic if I’d reached this point in my life and I hadn’t. How else do you have longevity? There are so many guys who started out with me in radio who have disappeared because they can’t broaden their view of what entertainment should be, or get in touch with what they find to be exciting and fun and funny.”

Stern, 62, has not dropped the adults-only material, and the freedom of satellite radio allows him and his crew to indulge an unconditional love for profanity. But he seems warmer now and his interest in people has never had greater depth or range. The interviews give the show a heft that it didn’t formerly have, turning his New York studio at SiriusXM into a destination of choice for those who a decade ago might have steered clear.

“Today, if you go on a TV talk show and give a great six or seven minutes, people will link to it if it’s incredible,” said Lewis Kay, who oversees media for Tracy Morgan, Amy Poehler and others. “But if you kill on Stern, it moves the needle.”

Revelations on the show sometimes make news, as happened last year when “Modern Family” star Sofia Vergara discussed the feud with her ex-husband over frozen embryos. But more often, Stern just elicits the most interesting version of his visitors, through curiosity, patience and the benefits of huge and commercial-free blocks of time.

Conan O’Brien described himself on the show as “somewhat medicated” in a discussion about his low-level depression. Lady Gaga talked about the days she used to snort cocaine all by herself while she wrote music. John Goodman admitted that he turned up drunk a few times on the set of “The Big Lebowski.”

Stern believes his approach isn’t just better radio, it’s also better for whatever product his guest is promoting.

“If someone comes in and the audience feels like ‘Oh my God, I love this person,’ they will want to see their movie,” he said. “It’s a strange thing to say to someone trained in PR, but it’s the God’s honest truth. If someone has an hour to sit and talk about their life and at the end they say, ‘By the way, that’s what brought me to this movie, or to write this book,’ it’s such a powerful vehicle for promotion.”

Some worried that Stern would disappear once he went off free-to-air radio, and for many he did. But Sirius — now SiriusXM, after merging with its biggest rival — currently has 30 million subscribers. Exactly how many are listening to Stern the company won’t say, but his chops as an interviewer are a significant part of his appeal.

This is especially true in Los Angeles, where meetings have been known to be delayed because people are sitting in the parking lot, waiting for the last question. “One of the most common conversations I have about Howard is something like, ‘I was stuck in my car because Sia was on,’ or ‘He was finishing up an interview with Jeff Bridges,’ ” said Jeff Probst, the host of “Survivor” and self-described Stern superfan.

“Among showbiz types, being a Stern fan is something like belonging to a secret society,” said Andy Richter, the longtime sidekick of O’Brien. “So when I bump into someone like, say, Jonah Hill, one of us will invariably say ‘Did you hear Stern interview?’ — and then you fill in the blank of the last big interview he did.”

Stern still claims on the show to be an anxious mess, but he sounds calmer and more content. He plainly roots for all his guests and his questions reflect sensitivities unimaginable even a few years ago. Recently, he asked Tina Fey if “Who are you wearing?” is a sexist question to ask women red-carpeting at the Oscars. (Nah, she said.) Lena Dunham called him “an outspoken feminist” on “The Tonight Show.”

This is the same guy who, for years, traded misogynistic quips with anyone, including Donald Trump. In a 2005 phone interview, the two rated the looks of the cast of “Desperate Housewives.”

Pinpointing when Stern started his deep interview phase isn’t easy. It certainly was after he joined Sirius and it has intensified in the last 21/2 years, according to his longtime producer, Gary Dell’Abate.

“We never sat down and said, ‘This is what we’re going to do,’ ” he said. “It was organic. The caliber of guests got a little better, Howard’s research got a little better, publicists out there started saying, ‘Wow, that was a great interview.’ ”

Friends and fans attribute Stern’s evolution in large part to his marriage in 2008 to Beth Ostrosky Stern, a former model who not only has left him lovestruck, but turned him into an animal rescue advocate. Serving as a judge on NBC’s “America’s Got Talent,” which he did for four years, also proved that his days as an outsider scrabbling for mainstream credibility were behind him.

“For a long time, he was an underdog, he was always fighting the establishment,” Probst said. “Being a judge on ‘America’s Got Talent’ said to him, ‘You are deserving, you are legitimate.’ I think it is one reason Howard said to himself, ‘OK, people really do like me. People really respect me.’ And maybe that chip on his shoulder is gone.”

Therapy has also been key. For years, Stern was in four-times-a-week psychoanalysis, as he frequently reminds listeners. (He’s since cut back.) Not only has this given him a modicum of inner peace, it has provided him with a set of tools that he uses on guests.

No set schedule is kept for interviews, which Stern conducts Monday through Wednesday, the only days he now works, after a contract renegotiation in 2011. To prepare, he and a couple of staffers will read and compile notes over the course of days. Stern might strategize for as long as a week, figuring out what he would want to hear if he were listening. Right before the interview begins, a point man will read aloud the team’s collective jottings.

“And then it just sticks in my head and I memorize it,” Stern said. “I don’t love the process. I get very anxious and uncomfortable because I want it to be so good. I want the audience to enjoy it, I want the performer to feel comfortable.”

While chunks of the show are more grown up than ever, sex and strippers remain a preoccupation. The Wack Pack, an unpaid and rotating cast of eccentrics, still have plenty of time to heckle one another and the staff, though some have been rechristened with less offensive names. Prank phone calls remain a staple. Not long ago, a Hillary Clinton sound-alike called a skywriting company and asked if it would spell out a derogatory slogan about Bernie Sanders’ bathroom habits.

Still, the show now includes enough lengthy interviews, delving into enough serious topics, to annoy some longtime fans. They fume on Reddit. They also call the show. Stern will occasionally put them on the air and let them vent. Enough with the talk about regrets and depression, they will say. We want naked women.