A modular disk coextrusion die is formed of a plurality of cells stacked together. Each cell includes an arrangement of thin annular disks, including at least a first cap disk, a first distribution disk, a first transition disk and a first spreader disk. The modular disk coextrusion die includes at least one channel disk having at least one inlet opening and at least two outlet openings per inlet opening. The thin annular disks are configured so that a first of the outlet openings of the channel disk is in fluid communication with the first distribution disk in the first cell and a second of the outlet openings in the channel disk is in fluid communication with the first distribution disk in the second cell. The channel disk provides for a more efficient utilization of space at the inlet of the modular disk coextrusion die and enables the feeding of up to twenty melt streams.