Not all first person accounts focus only on the character telling the story, so that option could still be in the running if you want to give it another try. In F. Scott Fitzgerald’s novel The Great Gatsby, for example, Nick Carraway tells Jay Gatsby’s story, while also covering a bit about his own experience. (In this case, the story is clearly Gatsby’s, but by the nature of Nick’s role, he also figures prominently. This point of view strategy—where a first person narrator tells another character’s story—is called first person peripheral.) When using first person to tell a broader story, there’s bound to be some differences in how much each character is emphasized. It might be best for a story where one character has a particularly unique perspective on the events or his perspective helps manage tension or direct the story in some way.
You have other choices, as well. First person plural tells a story through the collective “we” instead of the singular “I.” Jeffrey Eugenides chose this approach for his novel The Virgin Suicides, in which a group of boys—grown men at the telling of the story—attempt to understand five sisters. Here, the boys arrive for a party at the girls’ house, an event encouraged by a psychiatrist after the youngest daughter’s suicide attempt:
We were directed downstairs to the rec room. . . . On a card table, the punch bowl erupted lava. The paneled walls gleamed, and for the first few seconds the Lisbon girls were only a patch of glare like a congregation of angels. Then, however, our eyes got used to the light and informed us of something we had never realized: the Lisbon girls were all different people. Instead of five replicas with the same blond hair and puffy cheeks we saw that they were distinct beings, their personalities beginning to transform their faces and reroute their expressions.
There are moments where a character of this collective voice is briefly singled out, such as this one, when they approach the Lisbon’s house for party:
Then the night arrived. In blue blazers, with khaki trousers and clip-on neckties, we walked along the sidewalk in front of the Lisbon house as we had so many times before, but this time we turned up the walk, and climbed the front steps between the pots of red geraniums, and rang the doorbell. Peter Sissen acted as our leader, and even looked slightly bored, saying again and again, "Wait'll you see this."
This approach might be appropriate if the characters all have a very similar experience of the events.
You can also use first person serial, which is a series of first person singular perspectives that all work together to tell a story. The Sweet Hereafter, a novel by Russell Banks, is one of my favorite examples of this technique. It’s the story of a town in the aftermath of losing most of its children in a school bus accident. The first and last chapters are told in first person from the perspective of Delores Driscoll, the driver of the bus. In between, there are chapters from the first person perspective of Billy Ansel, a father who lost his children in the accident, Mitchell Stephens, a lawyer who comes to town in search of a lawsuit, and Nichole Burnell, a young girl who survives the accident. This approach gives you the ability to take a close look at the individual experience, but also allows you to explore the story with a broader scope. You might choose this approach if each character has something important or unique to add to the experience of the larger story.