Deterministic lateral displacement (DLD) devices separate micrometer-scale particles in solution based on their size using a laminar microfluidic flow in an array of obstacles. We investigate array geometries with rational row-shift fractions in DLD devices by use of a simple model including both advection and diffusion. Our model predicts novel multi-directional sorting modes that could be experimentally tested in high-throughput DLD devices containing obstacles that are much smaller than the separation between obstacles.