Danny Elfman, who has composed some of the most beloved fan-favorite films of the last few decades, was brought in to do the Justice League film, Elfman, who talks about the project in the video below, tells of the complexity of having six different main characters and trying to pay homage to the legacy of the DC films through music. He refers to the project as fun, but also a jigsaw puzzle to solve. He pulled on elements from the John Williams Superman Theme, the Hans Zimmer Wonder Woman theme and even his own work on the 1989 Batman film.
He also points out that instead of giving Aquaman, Flash and Cyborg their own themes, he gave them their own sound that would be incorporated into the music. If he had done unique themes for each he would then be running six themes, meaning he'd be playing on of those themes almost all the time in the film.
He also talks about creating a theme for the Justice League as a whole and how it was the most fun for him because he wanted to tie all the characters together into this one theme. A theme for all of them but for none of them individually.
Justice League is in theaters now.