One other small detail noted in the South and Keen weddings was the elimination of any mention of “forsaking all others” in the ceremony. At the same time, neither couple put anything in their self-written vows about continuing to keep their relationship open. The closest the Keens came was in a speech Ms. Keen gave during the reception.

“I wrote a poem and in there I said something about how many people are a part of our relationship, no one picked up on it,” she recalled.

Other than that, all of these weddings were a lot like any other wedding you’d get invited to or hear about. “We wanted the wedding to be a complete showcase of who we are as a couple,” Ms. South said. “We wanted people to walk in and immediately say, ‘Yep, this is Logan and Daley,’” Mr. South said. That meant having a twin flame ceremony, custom dishes (Mr. South’s request) and no first look. “It was super important to me to have the first time we saw each other at the end of the aisle,” Ms. South said.

Image “This relationship felt to both of us not like a trap, not like this impossible set of ideals that you have to live up to,” said Ms. Keen who is in a three-person relationship with her husband and their girlfriend. Credit... Voyteck Photography

For the Keens, that meant getting married at Chelsea Town Hall in London, riding off on bikes with water bottles tied to the back wearing leather jackets with “Just Married” written on them and having a big party at a club with hundreds of guests. But most symbolically, it also meant incorporating nature, because “this is the most natural relationship either of us have ever had,” Ms. Keen said. When they decided to “open” their relationship, she said, it was “natural.” After their town hall ceremony, they had another ceremony that 120 friends and family members attended at Wormholt Park in London. When they said their vows, they took off their shoes.

“It felt right, this relationship felt to both of us not like a trap, not like this impossible set of ideals that you have to live up to, which I really felt in previous relationships and so did he,” Ms. Keen said. “So, we took it out of a church, we got rid of the whole pomp and procedure, and we made it about family and our son and about the earth and the moment.”