Abstract: We present a camera with switchable primaries using shiftable layers of color filter arrays (CFAs). By layering a pair of CMY CFAs in this novel manner we can switch between multiple sets of color primaries (namely RGB, CMY and RGBCY) in the same camera. In contrast to fixed color primaries (e.g. RGB or CMY), which cannot provide optimal image quality for all scene conditions, our camera with switchable primaries provides optimal color fidelity and signal to noise ratio for multiple scene conditions. par Next, we show that the same concept can be used to layer two RGB CFAs to design a camera with switchable low dynamic range (LDR) and high dynamic range (HDR) modes. Further, we show that such layering can be generalized as a constrained satisfaction problem (CSP) allowing to constrain a large number of parameters (e.g. different operational modes, amount and direction of the shifts, placement of the primaries in the CFA) to provide an optimal solution. par We investigate practical design options for shiftable layering of the CFAs. We demonstrate these by building prototype cameras for both switchable primaries and switchable LDR/HDR modes. par To the best of our knowledge, we present, for the first time, the concept of shiftable layers of CFAs that provides a new degree of freedom in photography where multiple operational modes are available to the user in a single camera for optimizing the picture quality based on the nature of the scene geometry, color and illumination.