Multistream heat exchangers (MHEXs) facilitate simultaneous heat exchange between multiple streams and are mainly used in energy-intensive cryogenic processes. Reducing the energy consumption of existing processes with MHEXs is important, but system-wide operational optimization necessitates that the heat-transfer parameters of the MHEXs are known. However, most MHEXs are practically black-boxes due to their proprietary designs and complex geometry. In this work, we present a procedure for the operational optimization of processes with MHEXs. Our procedure involves the development of a predictive model for MHEXs as the first step, followed by the illustration of operational optimization. We begin with the development of a data-driven nonlinear programming (NLP) model to synthesize an equivalent network of simple two-stream heat exchangers that best represents the operation of an MHEX. We then demonstrate our predictive modeling procedure on the main cryogenic heat exchanger (MCHE) from an existing natural gas liquefaction plant. Finally, we use the equivalent network of two-stream exchangers in the operational optimization of an example C3MR process.