Metasurfaces have drawn considerable attention in manipulation of electromagnetic waves due to their exotic subwavelength footprints. Regardless of immense progress of polarization-dependent flat optics, the realization of on-device switchable complete phase multiplication is still missing from design multifunctional devices. Here, by combining geometric and propagation phases, a generalized design principle is proposed that can achieve switchable integer or fractional multiple complete phase modulation in transmitted circularly cross-polarized light by switching the handedness of incident polarization. As a proof of concept, two types of spin-dependent bifunctional wavefront manipulating devices, including switchable beam splitter/beam deflector and spin-to-orbital angular momentum converter designs are numerically realized. It is believed that the proposed single-cell spin-switchable rational-multiple complete-phase-modulation design principle based on combined propagation and geometric phases has great potential to underpin the development of meta-optics-based multifunctional operations in the field of integrated optics, imaging, and optical communication.