Two of my favorite bands fit what you're looking for:
Coheed and Cambria - 9/10 of their records follow an ongoing Sci-Fi story. The most recent two albums just started a new chapter in that story.
The Dear Hunter - Like Coheed, the bulk of their Discography (The Acts) are one story. The just started a new, unrelated story with their latest record.
zorton213 t1_j1v21va wrote
Reply to Modern rock concept albums that tell a story by condog1035
Two of my favorite bands fit what you're looking for:
Coheed and Cambria - 9/10 of their records follow an ongoing Sci-Fi story. The most recent two albums just started a new chapter in that story.
The Dear Hunter - Like Coheed, the bulk of their Discography (The Acts) are one story. The just started a new, unrelated story with their latest record.