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Ensuring fairness is crucial in developing modern algorithms and tests. To address potential biases and discrimination in algorithmic decision making, researchers have drawn insights from the test fairness literature, notably the work on differential algorithmic functioning (DAF) by Suk and Han. Nevertheless, the exploration of intersectionality in fairness investigations, within both test fairness and algorithmic fairness fields, is still relatively new. In this paper, we propose an extension of the DAF framework to include the concept of intersectionality. Similar to DAF, the proposed notion for intersectionality, which we term “interactive DAF,” leverages ideas from test fairness and algorithmic fairness. We also provide methods based on the generalized Mantel–Haenszel test, generalized logistic regression, and regularized group regression to detect DAF, interactive DAF, or other subtypes of DAF. Specifically, we employ regularized group regression with three different penalties and examine their performance via a simulation study. Finally, we demonstrate our intersectional DAF framework in real-world applications on grade retention and conditional cash transfer programs in education.