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Motivated by the growing importance of reducing unfairness in ML predictions, Fair-ML researchers have presented an extensive suite of algorithmic 'fairness-enhancing' remedies. Most existing algorithms, however, are agnostic to the sources of the observed unfairness. As a result, the literature currently lacks guiding frameworks to specify conditions under which each algorithmic intervention can potentially alleviate the underpinning cause of unfairness. To close this gap, we scrutinize the underlying biases (e.g., in the training data or design choices) that cause observational unfairness. We present the conceptual idea and a first implementation of a bias-injection sandbox tool to investigate fairness consequences of various biases and assess the effectiveness of algorithmic remedies in the presence of specific types of bias. We call this process the bias(stress)-testing of algorithmic interventions. Unlike existing toolkits, ours provides a controlled environment to counterfactually inject biases in the ML pipeline. This stylized setup offers the distinct capability of testing fairness interventions beyond observational data and against an unbiased benchmark. In particular, we can test whether a given remedy can alleviate the injected bias by comparing the predictions resulting after the intervention in the biased setting with true labels in the unbiased regime-that is, before any bias injection. We illustrate the utility of our toolkit via a proof-of-concept case study on synthetic data. Our empirical analysis showcases the type of insights that can be obtained through our simulations.