Counterfactual‐model‐based mediation analysis can yield substantial insight into the causal mechanism through the assessment of natural direct effects (NDEs) and natural indirect effects (NIEs). However, the assumptions regarding unmeasured mediator‐outcome confounding and intermediate mediator‐outcome confounding that are required for the determination of NDEs and NIEs present practical challenges. To address this problem, we introduce an instrumental blocker, a novel quasi‐instrumental variable, to relax both of these assumptions, and we define a swapped direct effect (SDE) and a swapped indirect effect (SIE) to assess the mediation. We show that the SDE and SIE are identical to the NDE and NIE, respectively, based on a causal interpretation. Moreover, the empirical expressions of the SDE and SIE are derived with and without an intermediate mediator‐outcome confounder. Then, a multiply robust estimation method is derived to mitigate the model misspecification problem. We prove that the proposed estimator is consistent, asymptotically normal, and achieves the semiparametric efficiency bound. As an illustration, we apply the proposed method to genomic datasets of lung cancer to investigate the potential role of the epidermal growth factor receptor in the treatment of lung cancer.