Modern manufacturing value chains require intelligent orchestration of processes across company borders in order to maximize profits while fostering social and environmental sustainability. However, the implementation of integrated, systems-level approaches for data-informed decision-making along value chains is currently hampered by privacy concerns associated with cross-organizational data exchange and integration. We here propose Privacy-Preserving Partial Least Squares (P3LS) regression, a novel federated learning technique that enables cross-organizational data integration and process modeling with privacy guarantees. P3LS involves a singular value decomposition (SVD) based PLS algorithm and employs removable, random masks generated by a trusted authority in order to protect the privacy of the data contributed by each data holder. We demonstrate the capability of P3LS to vertically integrate process data along a hypothetical value chain consisting of three parties and to improve the prediction performance on several process-related key performance indicators. Furthermore, we show the numerical equivalence of P3LS and PLS model components on simulated data and provide a thorough privacy analysis of the former. Moreover, we propose a mechanism for determining the relevance of the contributed data to the problem being addressed, thus creating a basis for quantifying the contribution of participants.