This study explores in detail design options and simulations of multi-junction solar cells that utilize silicon-germanium-tin (SixGe1-x-ySny or SiGeSn) to achieve high-efficiency solar power conversion devices. SixGe1-x-ySny is an emerging system of alloys that can lattice match with germanium and gallium arsenide and can provide a bandgap higher than that of germanium; useful in the development of multi-junction solar cells. The results herein include designs of four devices: a triple-junction, a quadruple-junction, a seven-junction, and a six-junction, with estimated efficiencies of 41.6%, 42.6%, 41.2%, and 39.2% respectively under 1000x concentrated AM1.5D illumination, where the seven- and six-junction devices relax the thickness requirement of the germanium layer, and have room for improvement via the development of an advanced tunnel-junction component. Visualizations of the potentially available SiGeSn bandgaps are developed. The documentation supports further work in modelling additional compositions of SiGeSn. Loss mechanisms of the devices are calculated and plotted, enabling the design of the device layer components. Tools and techniques are developed to determine and control the resultant output error, and a generalized simulation mesh definition is given that efficiently controls the primary source of error of the calculation, which is related to the optical interaction. Lateral currents and surface recombination effects are included. The software is modularized to enable the development of higher-order segmented devices.