When cyclically driven, certain disordered materials exhibit transient and multiperiodic responses that are difficult to reproduce in synthetic materials. Here, we show that elementary multiperiodic elements with period T = 2 — togglerons—can serve as building blocks for such responses. We experimentally realize metamaterials composed of togglerons with tunable transients and periodic responses-including odd periods. Our approach suggests a hierarchy of increasingly complex elements in frustrated media, and opens a new strategy for rational design of sequential metamaterials.