Real-world machine learning applications often involve data from multiple modalities that must be integrated effectively to make robust predictions. However, in many practical settings, not all modalities are available for every sample, and acquiring additional modalities can be costly. This raises the question: which samples should be prioritized for additional modality acquisition when resources are limited? While prior work has explored individual-level acquisition strategies and training-time active learning paradigms, test-time and cohort-based acquisition remain underexplored despite their importance in many real-world settings. We introduce Cohort-based Active Modality Acquisition (CAMA), a novel test-time setting to formalize the challenge of selecting which samples should receive additional modalities. We derive acquisition strategies that leverage a combination of generative imputation and discriminative modeling to estimate the expected benefit of acquiring missing modalities based on common evaluation metrics. We also introduce upper-bound heuristics that provide performance ceilings to benchmark acquisition strategies. Experiments on common multimodal datasets demonstrate that our proposed imputation-based strategies can more effectively guide the acquisition of new samples in comparison to those relying solely on unimodal information, entropy guidance, and random selections. Our work provides an effective solution for optimizing modality acquisition at the cohort level, enabling better utilization of resources in constrained settings.