Gene regulation networks allow organisms to adapt to diverse environmental niches. However, the constraints underlying the evolution of gene regulation remain ill defined. Here, we show that partial order-a concept that ranks network output levels as a function of different input signals-identifies such constraints. We tested our predictions by experimentally evolving an engineered signal-integrating network in multiple environments. We find that populations: (1) expand in fitness space along the Pareto-optimal front associated with conflicts in regulatory demands, by fine-tuning binding affinities within the network, and (2) expand beyond the Pareto-optimal front through changes in the network structure. Our constraint predictions are based only on partial order and do not require information on the network architecture or underlying genetics. Overall, our findings show that limited knowledge of current regulatory phenotypes can provide predictions on future evolutionary constraints.