Mass exchanger networks (MENs) are used to remove/recover contaminants from polluted streams through absorption with available process streams or external mass separating agents. Process Integration techniques such as Pinch Technology (PT) or mathematical optimisation can be used to synthesise optimal networks, however a lack of accessible software and difficulties in formulating the non-convex problem has stunted research. This article presents an open-source Python package for the synthesis of optimal MENs. The package uses the algebraic modelling language, Pyomo, and takes advantage of Python’s object-oriented nature to solve a series of optimisation problems, improving on the performance of previous approaches to the problem of incorporating detailed unit designs into MEN synthesis. The package uses automated initialisation strategies to first solve a superstructure-based mixed-integer nonlinear program (MINLP). Thereafter, a detailed optimisation model, formulating the packed column as a system of differential-algebraic equations, is used to design the columns. This detailed packed column design is used to update the MINLP through correction factors, driving the network solution towards the detailed unit optimisation solutions. The new software, called MExNetS, implements this strategy in a user-friendly package that is easily modified and well-documented. In addition to the new software implementation, novel strategies are employed to ensure feasibility at each iteration, which is a challenge in these non-convex optimisation formulations, and new binary cuts are generated and applied to the MINLP that can significantly speed up convergence compared to the previous study. The package also contains automatic superstructure generation based on user-inputted data, with the hope that this software can inspire further research in this area and be accessible to practitioners.