Currently, researchers have paid great attention to retrieval-based dialogues in open-domain. In particular, people study the problem by investigating context-response matching for multi-turn response selection based on publicly recognized benchmark data sets. State-of-the-art methods require a response to interact with each utterance in a context from the beginning, but the interaction is performed in a shallow way. In this work, we let utterance-response interaction go deep by proposing an interaction-over-interaction network (IoI). The model performs matching by stacking multiple interaction blocks in which residual information from one time of interaction initiates the interaction process again. Thus, matching information within an utterance-response pair is extracted from the interaction of the pair in an iterative fashion, and the information flows along the chain of the blocks via representations. Evaluation results on three benchmark data sets indicate that IoI can significantly outperform state-of-the-art methods in terms of various matching metrics. Through further analysis, we also unveil how the depth of interaction affects the performance of IoI.