Advances in experimental techniques resulted in abundant genomic, transcriptomic, epigenomic, and proteomic data that have the potential to reveal critical drivers of human diseases. Complementary algorithmic developments enable researchers to map these data onto protein-protein interaction networks and infer which signaling pathways are perturbed by a disease. Despite this progress, integrating data across different biological samples or patients remains a substantial challenge because samples from the same disease can be extremely heterogeneous. Somatic mutations in cancer are an infamous example of this heterogeneity. Although the same signaling pathways may be disrupted in a cancer patient cohort, the distribution of mutations is long-tailed, and many driver mutations may only be detected in a small fraction of patients. We developed a computational approach to account for heterogeneous data when inferring signaling pathways by sharing information across the samples. Our technique builds upon the prize-collecting Steiner forest problem, a network optimization algorithm that extracts pathways from a protein-protein interaction network. We recover signaling pathways that are similar across all samples yet still reflect the unique characteristics of each biological sample. Leveraging data from related tumors improves our ability to recover the disrupted pathways and reveals patient-specific pathway perturbations in breast cancer.