Exploratory data analysis of high-dimensional datasets is a crucial task for which visual analytics can be especially useful. However, the ad hoc nature of exploratory analysis can also lead users to draw incorrect causal inferences. Previous studies have demonstrated this risk and shown that integrating counterfactual concepts within visual analytics systems can improve users’ understanding of visualized data. However, effectively leveraging counterfactual concepts can be challenging, with only bespoke implementations found in prior work. Moreover, it can require expertise in both counterfactual subset analysis and visualization to implement the functionalities practically. This paper aims to help address these challenges in two ways. First, we propose an operator-based conceptual model for the use of counterfactuals that is informed by prior work in visualization research. Second, we contribute the Co-op library, an open and extensible reference implementation of this model that can support the integration of counterfactual-based subset computation with visualization systems. To evaluate the effectiveness and generalizability of Co-op, the library was used to construct two different visual analytics systems each supporting a distinct user workflow. In addition, expert interviews were conducted with professional visual analytics researchers and engineers to gain more insights regarding how Co-op could be leveraged. Finally, informed in part by these evaluation results, we distil a set of key design implications for effectively leveraging counterfactuals in future visualization systems.