Deep reduction in industrial greenhouse gas emissions can be achieved through engineering measures such as energy efficiency enhancement, fuel switching, and carbon dioxide removal (CDR). Integrated energy systems like polygeneration plants are inherently efficient, while partial or total replacement of fossil fuels with renewables allows further cuts to be realized. Novel CDR technologies can also be used to generate negative emissions. In this work, we develop an optimization model for optimizing a novel polygeneration system which integrates CDR based on ex situ enhanced rock weathering. The latter relies on exposing pulverized rock to accelerate naturally occurring geochemical reactions of minerals with ambient carbon dioxide and water, and results in the sequestration of carbon as bicarbonate ions in water. Integration with a polygeneration plant allows surplus electricity to be utilized for the energy-intensive rock grinding process, as an alternative to direct energy storage. A mixed-integer linear programming enterprise input-output (MILP-EIO) model is developed and then applied to a case study on design and operation problem. The objective is to determine the optimal design of a zero emissions polygeneration system which is economically feasible. Results indicate that such a result is only possible once CO2 price reaches at least US$ 50 /t.