We investigate the general adjustment of projection-based phase retrieval algorithms for use with saturated data. In the phase retrieval problem, model fidelity of experimental data containing a non-zero background level, fixed pattern noise, or overexposure, often presents a serious obstacle for standard algorithms. Recently, it was shown that overexposure can help to increase the signal-to-noise ratio in AI applications. We present our first results in exploring this direction in the phase retrieval problem, using as an example the Gerchberg-Saxton algorithm with simulated data. The proposed method can find application in microscopy, characterisation of precise optical instruments, and machine vision applications of Industry4.0.