Synthesization of multiple functionalities over a flat metasurface platform offers a promising approach to achieving integrated photonic devices with minimized footprint. Metasurfaces capable of diverse wavefront shaping according to wavelengths and polarizations have been demonstrated. Here we propose a class of angle-selective metasurfaces, over which beams are reflected following different and independent phase gradients in the light of the beam direction. Such powerful feature is achieved by leveraging the local phase modulation and the non-local lattice diffraction via inverse scattered field and geometry optimization in a monolayer dielectric grating, whereas most of the previous designs utilize the local phase modulation only and operate optimally for a specific angle. Beam combiner/splitter and independent multibeam deflections with up to 4 incident angles are numerically demonstrated respectively at the wavelength of 700 nm. The deflection efficiency is around 45% due to the material loss and the compromise of multi-angle responses. Flexibility of the approach is further validated by additional designs of angle-switchable metagratings as splitter/reflector and transparent/opaque mirror. The proposed designs hold great potential for increasing information density of compact optical components from the degree of freedom of angle.