Abstract Geometric-phase metasurfaces, recently utilized for controlling wavefronts of circular polarized (CP) electromagnetic waves, are drastically limited to the cross-polarization modality. Combining geometric with propagation phase allows to further control the co-polarized output channel, nevertheless addressing only similar functionality on both co-polarized outputs for the two different CP incident beams. Here we introduce the concept of chirality-assisted phase as a degree of freedom, which could decouple the two co-polarized outputs, and thus be an alternative solution for designing arbitrary modulated-phase metasurfaces with distinct wavefront manipulation in all four CP output channels. Two metasurfaces are demonstrated with four arbitrary refraction wavefronts, and orbital angular momentum modes with four independent topological charge, showcasing complete and independent manipulation of all possible CP channels in transmission. This additional phase addressing mechanism will lead to new components, ranging from broadband achromatic devices to the multiplexing of wavefronts for application in reconfigurable-beam antenna and wireless communication systems.