Networks appear naturally in many high-impact real-world applications. In an increasingly connected and coupled world, the networks arising from many application domains are often collected from different channels, forming the so-called multi-layered networks, such as cyber-physical systems, organization-level collaboration platforms, critical infrastructure networks and many more. Compared with single-layered networks, multi-layered networks are more vulnerable as even a small disturbance on one supporting layer/network might cause a ripple effect to all the dependent layers, leading to a catastrophic/cascading failure of the entire system. The state-of-the-art has been largely focusing on modeling and manipulating the cascading effect of two-layered interdependent network systems for some specific type of network connectivity measure. This paper generalizes the challenge to multiple dimensions. First, we propose a new data model for multi-layered networks MULAN, which admits an arbitrary number of layers with a much more flexible dependency structure among different layers, beyond the current pair-wise dependency. Second, we unify a wide range of classic network connectivity measures SUBLINE. Third, we show that for any connectivity measure in the SUBLINE family, it enjoys the diminishing returns property which in turn lends itself to a family of provable near-optimal control algorithms with linear complexity. Finally, we conduct extensive empirical evaluations on real network data, to validate the effectiveness of the proposed algorithms.