In recommender systems, a common problem is the presence of various biases in the collected data, which deteriorates the generalization ability of the recommendation models and leads to inaccurate predictions. Doubly robust (DR) learning has been studied in many tasks in RS, with the advantage that unbiased learning can be achieved when either a single imputation or a single propensity model is accurate. In this paper, we propose a multiple robust (MR) estimator that can take the advantage of multiple candidate imputation and propensity models to achieve unbiasedness. Specifically, the MR estimator is unbiased when any of the imputation or propensity models, or a linear combination of these models is accurate. Theoretical analysis shows that the proposed MR is an enhanced version of DR when only having a single imputation and propensity model, and has a smaller bias. Inspired by the generalization error bound of MR, we further propose a novel multiple robust learning approach with stabilization. We conduct extensive experiments on real-world and semi-synthetic datasets, which demonstrates the superiority of the proposed approach over state-of-the-art methods.