A modular disk coextrusion die is formed of a plurality of cells stacked together. Each cell includes a symmetrical arrangement of thin annular disks, including a central routing disk and two distribution disks on both sides of the central routing disk. The distribution disks are oriented so that their respective distribution inlet openings oppose each other by about 180 degrees. The symmetrical arrangement permits each cell to process the melt streams in a manner that provides enhanced layer uniformity and bubble stability. By stacking several cells, blown films having up to several hundred layers can be made using twelve, twenty-four or more polymer melt streams.