Eukaryotic genes are regulated by multivalent transcription factor complexes. Through cooperative self-assembly, these complexes perform nonlinear regulatory operations involved in cellular decision-making and signal processing. In this study, we apply this design principle to synthetic networks, testing whether engineered cooperative assemblies can program nonlinear gene circuit behavior in yeast. Using a model-guided approach, we show that specifying the strength and number of assembly subunits enables predictive tuning between linear and nonlinear regulatory responses for single- and multi-input circuits. We demonstrate that assemblies can be adjusted to control circuit dynamics. We harness this capability to engineer circuits that perform dynamic filtering, enabling frequency-dependent decoding in cell populations. Programmable cooperative assembly provides a versatile way to tune the nonlinearity of network connections, markedly expanding the engineerable behaviors available to synthetic circuits.