Computational caustics and light steering displays offer a wide range of interesting applications, ranging from art works and architectural installations to energy efficient HDR projection. In this work we expand on this concept by encoding several target images into pairs of front and rear phase-distorting surfaces. Different target holograms can be decoded by mixing and matching different front and rear surfaces under specific geometric alignments. Our approach, which we call mix-and-match holography, is made possible by moving from a refractive caustic image formation process to a diffractive, holographic one. This provides the extra bandwidth that is required to multiplex several images into pairing surfaces.