Polarization transformation is at the foundation of modern applications in photonics and quantum optics. Notwithstanding their applicative interests, basic theoretical and experimental efforts are still needed to exploit the full potential of polarization optics. Here, we reveal that the coherent superposition of two non-orthogonal eigen-states of Jones matrix can improve drastically the efficiency of arbitrary polarization transformation with respect to classical orthogonal polarization optics. By exploiting metasurface with stacking and twisted configuration, we have implemented a powerful configuration, termed “non-orthogonal metasurfaces”, and have experimentally demonstrated arbitrary input-output polarization modulation reaching nearly 100% transmission efficiency in a broadband and angle-insensitive manner. Additionally, we have proposed a routing methodology to project independent phase holograms with quadruplex circular polarization components. Our results outline a powerful paradigm to achieve extremely efficient polarization optics, and polarization multiplexing for communication and information encryption at microwave and optical frequencies.