This paper considers the synthesis of refrigeration systems with refrigerant mixtures as working fluids. The employed refrigeration topology encompasses features from industrial liquefaction of natural gas (LNG) systems. This configuration consists of a combination of horizontal and vertical cascades generalizing the vertical cascade of pure refrigerant systems. The key features of mixtures exploited here are their ability to evaporate/condense over a temperature range and their potential to generate streams with different compositions through partial condensation. The synthesis problem is formulated and solved as a nonlinear program. The proposed methodology is illustrated using an example of cooling a methane-rich stream.