Multi-hop Question Generation (MQG) aims to create questions that require synthesizing multiple, dispersed pieces of supporting evidence from different passages. The fundamental challenge lies in the dependence among different reasoning steps where each step relies on the preceding one. Traditional approaches generally rely on learning observed dependency during the training process, which limits their adaptability to value-changed instances in the reasoning chains. To this end, we propose a model-agnostic method, termed CS2MQG, that employs Counterfactual Supporting with bridging dependency prototype invariance for Multi-hop Question Generation. Specifically, we focus on key bridging nodes with high centrality or rich contextual information. And then, the counterfactuals are systematically generated by keeping the node type while modifying its value. Through the reassignment of these nodes, new causal relationships will be introduced into models, ensuring the generated questions are accurately centered around these nodes. Experiments conducted on the widely used HotpotQA and MuSiQue datasets demonstrate that CS2MQG consistently improves the performance of five state-of-the-art MQG models in terms of BLEU, METEOR, and ROUGE scores. And, our counterfactuals also enhance the performance of zero-shot MQG.