Near-field radio holography is a common method for measuring and aligning mirror surfaces for millimeter and sub-millimeter telescopes. In instruments with more than a single mirror, degeneracies arise in the holography measurement, requiring multiple measurements and new fitting methods. We present HoloSim-ML, a Python code for beam simulation and analysis of radio holography data from complex optical systems. This code uses machine learning to efficiently determine the position of hundreds of mirror adjusters on multiple mirrors with few micron accuracy. We apply this approach to the example of the Simons Observatory 6m telescope.