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The “impossibility theorem” — which is considered foundational in algorithmic fairness literature — asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two special cases: when the prevalence of the outcome being predicted is equal across groups, or when a perfectly accurate predictor is used. However, theory does not always translate to practice. In this work, we challenge the implications of the impossibility theorem in practical settings. First, we show analytically that, by slightly relaxing the impossibility theorem (to accommodate a practitioner’s perspective of fairness), it becomes possible to identify abundant sets of models that satisfy seemingly incompatible fairness constraints. Second, we demonstrate the existence of these models through extensive experiments on five real-world datasets. We conclude by offering tools and guidance for practitioners to understand when — and to what degree — fairness along multiple criteria can be achieved. This work has an important implication for the community: achieving fairness along multiple metrics for multiple groups (and their intersections) is much more possible than was previously believed.