This paper explores how to efficiently combine multiple runtime monitors into a single monitoring protocol. The goal is to maximize the probability of applying safety measures (recall) for misaligned output. Because executing monitors and applying safety measures incur costs, we must adhere to the average-case budget constraint. We develop an algorithm that finds the optimal protocol by considering the performance and cost of existing monitors. This algorithm performs an exhaustive search to determine when and which monitors to invoke, and assigns safety measures based on the Neyman-Pearson lemma. By focusing on likelihood ratios and strategically trading off the costs of monitors and measures, we more than double the recall compared to baselines in a code review setting. We also demonstrate that combining two monitors yields a Pareto improvement over using a single monitor. This framework provides a principled methodology for combining existing monitors to detect undesirable behavior in cost-sensitive environments.