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Most of the contemporary approaches for multi-hop Natural Language Inference (NLI) construct explanations considering each test case in isolation. However, this paradigm is known to suffer from semantic drift, a phenomenon that causes the construction of spurious explanations leading to wrong conclusions. In contrast, this paper proposes an abductive framework for multi-hop NLI exploring the retrieve-reuse-refine paradigm in Case-Based Reasoning (CBR). Specifically, we present Case-Based Abductive Natural Language Inference (CB-ANLI), a model that addresses unseen inference problems by analogical transfer of prior explanations from similar examples. We empirically evaluate the abductive framework on commonsense and scientific question answering tasks, demonstrating that CB-ANLI can be effectively integrated with sparse and dense pre-trained encoders to improve multi-hop inference, or adopted as an evidence retriever for Transformers. Moreover, an empirical analysis of semantic drift reveals that the CBR paradigm boosts the quality of the most challenging explanations, a feature that has a direct impact on robustness and accuracy in downstream inference tasks.