Kitty Chambliss is already planning her Valentine’s Day. Her husband will make ravioli and roasted vegetables. She’ll bake a cheesecake.

Then she’ll seta table for three: her husband, herself and her boyfriend.

You may have noticed that polyamory is having a moment.

Pursuing multiple romantic, emotional or sexual relationships, with the permission of all involved—known as consensual non-monogamy—is increasingly out in the open, as adherents tout what they see as the benefits, such as more opportunities for emotional support and connectionas well assex.

There arechallenges, too, from the mundane—calendars—to the existential. First, there’s dating, just when you thought you’d put that hell behind you. It’s expensive: restaurants, hotels, cute outfits and even condoms add up. The scheduling could make a military planner sweat. More relationships mean more drama,from in-laws to breakups. Not to mention the lack of sleep.

I know what you’re thinking: Who has time for this?

Plenty of people, it turns out. Twenty-two percent of Americans say they have engaged in consensual non-monogamy, which is also sometimes called ethical non-monogamy, at some point in their life, according to a nationally representative study by researchers at the Kinsey Institute at Indiana University. That’s almost the same percentage—23%—as people living in the U.S. who have a bachelor’s degree as their highest degree.

Many more think about doing it. Research on sexual fantasies shows that nearly one-third of people in monogamous relationships report that being in some type of an open relationship is part of their favorite sexual fantasy. Eighty percent of those peoplesaid they’d act on the opportunity giventhe chance.

Open marriage buzz

This probably isn’t even the first thing you’ve read about the subject lately. A spate of podcasts, books and social-media accounts with hundreds of thousands of followers has brought polyamory to dinner conversations and coffee shops.

Molly Roden Winter, a wife and mother who lives in Brooklyn, N.Y., writes about her struggles, self-exploration (and busy sex life) in “More: A Memoir of Open Marriage.” The book,published this month, has received so much attention—much good, some judgy—that when I called her husband, Stewart Winter, for an interview and asked how he was, he blurted out: “Losing my will to live.”

Being the new face of non-monogamy isn’t easy.

Before their wedding 24 years ago, Stewart asked his wife to tell him if she was ever tempted to cheat on him. If that happens, he said, he might be OK with her sleeping with someone else as long as she was upfront with him about it. “I wanted the chance to fix what was broken,” he said.

Flash ahead almost a decade. Molly met a man and started “obsessing” about him. She told Stewart, and he told her to go for it.

“I was terrified,” says Molly, 51. “But I had to see what was there.”

Over the years, both spouses have dated, had lots of sex and formed long-term relationships with other people. They established rules, which have evolved over time. Some early ones that quickly fell by the wayside: no sleepovers, no falling in love, and Stewart wanted Molly to share details of her encounters and what she enjoys so he could learn more about what she likes.

“Maybe I never thought of dressing like a shepherd,” jokes Stewart, 56, a composer for TV and film.

The couple has confronted jealousy, tried therapy, learned how to process feelings and talk about their arrangement with family, friends and their sons, ages 18 and 21. They plan to stick with it, at least for now.

Molly says “it’s catapulted our marriage to the next level.”

Yes, there’s research

Most of the time when people talk about consensual non-monogamy they take one of two extreme perspectives, says Justin Lehmiller, a social psychologist and research fellow at the Kinsey Institute who studies sexual behavior. They say it will never work and that it is morally wrong. Or they claim that it is a morally superior, more evolved way of being. The truth is somewhere in between, he says.

One soon-to-be-published analysis of 26 studies found no differences in relationship satisfaction, sexual satisfaction, commitment or relationship length between those who practice consensual non-monogamy and those who are monogamous, says Amy Moors, an assistant professor of psychology at Chapman University and research fellow at the Kinsey Institute, who is lead author on the study.

People tend to be more committed to their primary partners in terms of building a life together and have more sex and more sexual satisfaction with their secondary ones, says Rhonda Balzarini, an assistant professor of psychology at Texas State University and research fellow at the Kinsey Institute, who has conducted research on this.

Asked by researchers about the downsides of pursuing multiple relationships, people described challenges such as the stigma, lack of legal recognition, communication and time-management issues. Wrote one participant: “Communication can be a pain.”

Chambliss, of the shared Valentine’s dinner, has been married for 18 years and with her boyfriend, whom she considers a full life partner, for eight. The three of them live together in Alexandria, Va.

A relationship coach who specializes in consensual non-monogamy, Chambliss, 54, says she enjoys traveling and discussing business with her husband; with her boyfriend, she talks philosophy and takes trips to the beach.

She says that she’s had arguments with her partners about miscommunications over scheduling. (A color-coded shared online calendar saved the day.) And there have been tough talks about deal breakers and insecurity. But Chambliss says the connection and sense of family far outweigh the challenges.

As for sleeping arrangements, Chambliss sometimes sleeps with her husband and sometimes spends the night with her boyfriend in his room.

“If I am sick of them both, I sleep in the guest room,” she says.

Write to Elizabeth Bernstein at Elizabeth.Bernstein@wsj.com