Directed self-assembly (DSA) of block copolymers is an emergent technique for nano-lithography, but is limited in the range of structures possible in a single fabrication step. Here we expand on traditional DSA chemical patterning. A blend of lamellar- and cylinder-forming block copolymers assembles on specially designed surface chemical line gratings, leading to the simultaneous formation of coexisting ordered morphologies in separate areas of the substrate. The competing energetics of polymer chain distortions and chemical mismatch with the substrate grating bias the system towards either line/space or dot array patterns, depending on the pitch and linewidth of the prepattern. This is in contrast to the typical DSA, wherein assembly of a single-component block copolymer on chemical templates generates patterns of either lines/spaces (lamellar) or hexagonal dot arrays (cylinders). In our approach, the chemical template encodes desired local spatial arrangements of coexisting design motifs, self-assembled from a single, sophisticated resist.