Cytoskeletal motors act as cargo transporters in cells1 and may be harnessed for directed transport applications in molecular detection and diagnostic devices2. High processivity — the ability to take many steps along a track before dissociating3 — is often a desirable characteristic because it allows nanoscale motors to transport cargoes over distances of microns in vivo and in vitro. Natural processive myosins4,5 are dimeric and use internal tension to coordinate the detachment cycles of the two heads6–8. Here, we show that processivity can be enhanced in engineered myosins using two non-natural strategies designed to optimize the effectiveness of random, uncoordinated stepping: (i) formation of three-headed and four-headed myosins; and (ii) introduction of flexible elements between heads. We quantify improvements using systematic single-molecule characterization of a panel of engineered motors. To test the modularity of our approach, we design a controllably bidirectional myosin that is robustly processive in both the forward and backward direction, and also produce the fastest processive cytoskeletal motor measured to date, reaching a speed of 10 μm/s.