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The importance of performing Level 3 probabilistic safety assessments (PSA) along with a general interest in assessing multi-unit risk has been sharply increasing after the Fukushima Daiichi nuclear power plant (NPP) accident. However, relatively few studies on multi-unit Level 3 PSA have been performed to date, reflecting limited scenarios of multi-unit accidents with higher priority. The major difficulty to carry out a multi-unit Level 3 PSA lies in the exponentially increasing number of multi-unit accident combinations, as different source terms can be released from each NPP unit; indeed, building consequence models for the astronomical number of accident scenarios is simply impractical. In this study, a new approach has been developed that employs the look-up table method to cover every multi-unit accident scenario. Consequence results for each scenario can be found on the table, established with a practical amount of effort, and can be matched to the frequency of the scenario. Preliminary application to a six-unit NPP site was carried out, where it was found that the difference between full-coverage and cut-off cases could be considerably high and therefore influence the total risk. Additional studies should be performed to fine tune the details and overcome the limitations of the approach. Keywords: Multi-unit risk, Multi-unit PSA, Site risk assessment, Level 3 PSA, Consequence analysis