Genetically engineering cells to perform customizable functions is an emerging frontier with numerous technological and translational applications. However, it remains challenging to systematically engineer mammalian cells to execute complex functions. To address this need, we developed a method enabling accurate genetic program design using high-performing genetic parts and predictive computational models. We built multifunctional proteins integrating both transcriptional and posttranslational control, validated models for describing these mechanisms, implemented digital and analog processing, and effectively linked genetic circuits with sensors for multi-input evaluations. The functional modularity and compositional versatility of these parts enable one to satisfy a given design objective via multiple synonymous programs. Our approach empowers bioengineers to predictively design mammalian cellular functions that perform as expected even at high levels of biological complexity.