It has been known that the robust behavior of a cellular signaling network is strongly related to the structural characteristics of the network, such as connectivity, the number of feedback loops, and the number of feed-forward loops. Previous studies proved such relationships through dynamical simulations of various random network models. Most of them, however, focused on robustness against a single node mutation. Considering that complex diseases such as cancer are mostly caused by simultaneous dysfunction of multiple genes, it is needed to investigate the robustness of a network against multiple node mutations. In this paper, we investigated the robustness of a network against multiple node mutations through extensive simulations on the basis of Boolean network models. We found that the robustness against multiple mutations is, in most cases, weaker than the robustness against a single node mutation on average. Moreover, we found that the robustness against multiple mutations is strongly positively correlated with the robustness against single mutation. The difference between the multiple- and single-mutation robustness became larger as the number of mutated nodes increased or the number of nodes that are robust to single-mutation decreased. We further found that a node of relatively large connectivity or being involved with many feedback loops tends to be non-robust against multiple mutations. This finding is supported by the observation that poly-genic disease genes have high connectivity and are involved with a large number of feedback loops than mono-genic disease genes in a human signaling network. Together, our study shows that previous studies for a single node mutation can be extended to understand the network dynamics for multiple node mutations.