A group that supports ethical non-monogamy sent an open letter to Meta on Thursday calling for Facebook to allow users to list more than one relationship status in their profiles.

The letter, which was initiated by the Organization for Polyamory and Ethical Non-monogamy, or OPEN, said that Facebook’s current policy is “arbitrary” and “exclusionary.” Signees included leaders of groups like the National Coalition for Sexual Freedom and the Center for Positive Sexuality.

A spokesman for Meta said the company was reviewing the letter and noted that one of the statuses that users can choose on Facebook is “in an open relationship.” The change the petitioners are asking for would allow them to list all of their romantic partners.

About 20 percent of people say they have engaged in some form of consensual non-monogamy, according to a 2017 study. Today, the term encompasses “a bajillion niche terms,” according to Brett Chamberlin, the executive director of OPEN. The most well-known terms include “polyamory,” which means dating multiple people at the same time, and “swinging,” which describes when people in relationships exchange partners with each other.

A newer entry is “relationship anarchy,” in which participants break down all the expected norms involved in romantic relationships and subscribe only to rules established by the people involved.

“Ethical non-monogamy is nothing new, but technologies like the internet have made it easier for people to build communities and pursue lifestyles that may not have been accepted in a mainstream culture before,” Mr. Chamberlin said.

Today, people interested in opening their relationships can turn to podcasts and polyamory coaches for advice, and join dating apps like Feeld and #open to meet like-minded others. Consensual non-monogamy has even reached Vogue magazine, where one writer asked: “Is Monogamy Over?”

People have become more public about their non-monogamous relationships, too, writing articles and social media posts about their experiences.

Last month, Taylor Frankie Paul, a TikTok star with 3.6 million followers, talked about her open marriage in a livestream. Ms. Paul, a member of the Mormon Church, told viewers that she and her husband and some of their friends would engage in “soft swinging,” in which “you don’t fully switch and go all the way.” Ms. Paul also said that she and her husband were currently in the process of getting a divorce, partly prompted by Ms. Paul’s decision to break the rules of their agreement.

The most prominent people who have publicly discussed their experiences with non-monogamy may be Will Smith and Jada Pinkett Smith. Last year Mr. Smith told GQ about a period during which his marriage was open.

“We have given each other trust and freedom, with the belief that everybody has to find their own way,” the actor said. “And marriage for us can’t be a prison.” Willow Smith, the couple’s daughter, spoke about being polyamorous on “Red Table Talk,” a show she hosts with her mother and grandmother.

Part of the shift toward more acceptance could be generational. In a YouGov poll that surveyed about 1,340 people and asked them to describe their “ideal relationship” along a scale from “completely monogamous” to “completely non-monogamous,” 43 percent of millennials said their ideal relationship would be at least somewhat non-monogamous, compared with 30 percent of Gen Xers and 25 percent of baby boomers.

Despite the growing normalization of non-monogamy as a practice, Mr. Chamberlin said, many people who engage in it still fear being public about their lifestyles.

“You could be fired from your job, denied housing or lose a custody battle based on the structure of your intimate relationships,” he said. The goal of his organization, which he and two others founded in April, is to raise awareness and create more acceptance of non-monogamous relationships.

“Over the long run, one of the projects of culture and society is giving people more space to be in the consensual relationships they choose,” he said. He pointed to the movement for L.G.B.T.Q. rights as one of those projects. Consensual non-monogamy, he added, “is the next chapter.”