We report a monochrome multi-task diffractive network architecture that leverages illumination phase multiplexing to dynamically reconfigure its output function and accurately implement a large group of complex-valued linear transformations between an input and output aperture. Each member of the desired group of T unique transformations is encoded and addressed with a distinct 2D illumination phase profile, termed "phase key", which illuminates the input aperture, activating the corresponding transformation at the output field-of-view. A common diffractive optical network, optimized with T phase keys, demultiplexes these encoded inputs and accurately executes any of the T distinct linear transformations at its output. We demonstrate that a diffractive network composed of N = 2 x T x Ni x No optimized diffractive features can realize T distinct complex-valued linear transformations, accurately executed for any complex field at the input aperture, where Ni and No refer to the input/output pixels, respectively. In our proof-of-concept numerical analysis, T = 512 complex-valued transformations are implemented by the same monochrome diffractive network with negligible error using illumination phase diversity. Compared with wavelength-multiplexed diffractive systems, phase-multiplexing architecture significantly lowers the transformation errors, potentially enabling larger-scale optical transformations to be implemented through a monochrome processor. Phase-multiplexed multi-task diffractive networks would enhance the capabilities of optical computing and machine-vision systems.