We introduce GestureRephaser, a novel motion synthesis framework that extends phase-based control to multiple body parts via independent phase manifolds. Building on the foundations of DeepPhase, which learns a global phase representation for periodic animation, our approach decomposes the body into semantically coherent parts (such as arms, spine, and legs) and assigns each a dedicated learned phase manifold. This design allows for asynchronous motion control, where different body parts can move in and out of sync with independent rhythmic structures, enabling complex and non-periodic full-body gestures. The system is driven entirely by phase variables and does not require audio, text, or semantic inputs, making it suitable for general-purpose character animation, looping motion editing, and interactive phase-based controllers. Extensive evaluations demonstrate that GestureRephaser achieves high motion realism, temporal consistency, and controllability, surpassing single-manifold models in flexibility and expressiveness.