Mirrors
1) A regular meeting of the JLA is interrupted when the team suddenly vanishes, replaced on Earth by their Crime Syndicate counterparts.
2) Disguising themselves as the League, the Syndicate begins to commit various acts of villainy.
3) A) During one such act, the JLI is called in to try and stop the League gone rogue. They fail.
B) Meanwhile, on the Syndicate’s Earth, the League is being hunted by the local Earth version of Damien Luthor and other “good” versions of villains from our Earth, the Heroic Society and other authorities.
4) A) Continuing its rampage across the country, the Syndicate battles the New Guardians, who are rather hopelessly outclassed.
B) The JLA battles with Luthor’s Heroic Society, which eventually comes to the realizations that these are not the villains they knew.
5) A) Continuing their rampage and plundering of tech, the Syndicate attacks a STAR Labs in San Diego and battles the Titans to a standstill.
B) Working together, the League and the Heroic Society discover the Syndicate’s headquarters and battle the members they left behind (perhaps based on other heroes from other teams), and find the machinery that sent them to their Earth, and are able to send them home.
6) The League returns to their proper dimension, but find the JSA waiting for them, not knowing they aren’t the rogue versions. The two teams battle. Just as they’re about to reach an understanding…
7) The Syndicate arrives, and takes down the JSA.
8) The League and Syndicate have an all-out battle, with the Syndicate being defeated and sent back to their own Earth.
9) The JLA will have some work to do restoring their reputation… (which can also be used for the JLI, to chain to them stepping up to fill that lack of trust void.)