Once you've beaten regular Story Mode, the character you used will be unlocked in the Another Story Mode.

Character	How to unlock
Arawn's Another Story	Beat Story Mode with Arawn.
Chizuru's Another Story	Beat Story Mode with Chizuru.
Hakuowlo's Another Story	Beat Story Mode with Hakuowlo.
Karulau's Another Story	Beat Story Mode with Karulau.
Konomi's Another Story	Beat Story Mode with Konomi.
Manaka's Another Story	Beat Story Mode with Manaka.
Morgan's Another Story	Beat Story Mode with Morgan.
Multi's Another Story	Beat Story Mode with Multi.
Oboro's Another Story	Beat Story Mode with Oboro.
Riannon's Another Story	Beat Story Mode with Riannon.
Sasara's Another Story	Beat Story Mode with Sasara.
Tamaki's Another Story	Beat Story Mode with Tamaki.
Touka's Another Story	Beat Story Mode with Touka.