Organisations are expected to develop sound strategies relating to their core operations capabilities of cost efficiency, quality, delivery, flexibility and innovation, to gain and maintain competitive advantage. However, there is a paucity of specific models that can be used to explain and predict how organisations combine and use these capabilities. Previous research has primarily focused on the ‘trade-off’ and the ‘cumulative capabilities’ models. In this study, data from an international sample of 1438 manufacturing plants are used to explore other models that organisations are using in addition to the two predominant models. This analysis shows that, in practice, the trade-off model is not used, but the cumulative capabilities model is used extensively. Further, our proposed new models, the ‘threshold’, ‘average’ and ‘multiple’, are prevalent in many plants. Also, a small proportion of the plants have in place the ‘uncompetitive’ model. In terms of relative effectiveness, there are no significant differences between the models with respect to several measures of operational performance. Overall, this study provides empirical evidence that there are other operations strategy models beyond the trade-off and cumulative capabilities dichotomy that organisations deploy.