Industrial decision-makers often base decisions on mathematical optimization models to achieve cost-efficient design solutions in energy transitions. However, since a model can only approximate reality, the optimal solution is not necessarily the best real-world energy system. Exploring near-optimal design spaces, e.g., by the Modeling All Alternatives (MAA) method, provides a more holistic view of decision alternatives beyond the cost-optimal solution. However, the MAA method misses out on discrete investment decisions. Incorporating such discrete investment decisions is crucial when modeling industrial energy systems. Our work extends the MAA method by integrating discrete design decisions. We optimize the design and operation of an industrial energy system transformation using a mixed-integer linear program. First, we explore the continuous, near-optimal design space by applying the MAA method. Thereafter, we sample all discrete design alternatives from the continuous, near-optimal design space. In a case study, we apply our method to identify all near-optimal design alternatives of an industrial energy system. We find 128 near-optimal design alternatives where costs are allowed to increase to a maximum of one percent offering decision-makers more flexibility in their investment decisions. Our work enables the analysis of discrete design alternatives for industrial energy transitions and supports the decision-making process for investments in energy infrastructure.