The documentary “There Is No ‘I’ in Threesome” (on HBO Max) begins with a couple stripping naked atop a high diving board. Giddy and clasping hands, they brace for the jump.

The director Jan Oliver Lucks, who goes by Ollie, and his fiancée Zoe are taking the plunge into an open relationship. Living on opposite sides of New Zealand, the long-distance duo are free to date and sleep with other people for a year leading up to their wedding. Using iPhones, they will each record the experience: Ollie hopes the documentary will make them poster children for an enriching alternative to monogamy.

Ollie and Zoe prove a sweet match, but as they coo and cuddle, they can be difficult to root for. Both are attention-seeking and excessively admiring of their project, and the home video of their hangouts tends toward indulgence. They may aim to present polyamory as tenable and fulfilling, but it comes off more as a risky experiment — particularly once Zoe’s fling with a theater director named Tom develops into a serious romance that strains her bond with Ollie.

But as our central couple’s connection falters, the documentary evolves into an astute examination of perspective. Zoe captures her own footage of her time with Tom, yet we begin to see her affair through Ollie’s eyes. As the film’s director and narrator, Ollie controls the story, and he uses this role to showcase his jealousy and his hurt. His cleverness culminates in the documentary’s startling final act, where Ollie shows how the artifice of filmmaking can mirror the lies we tell ourselves about love.

There Is No “I” in Threesome
Not rated. Running time: 1 hour 28 minutes. Watch on HBO Max.