Coordinate-transformation cloaking is based on the design of a metamaterial shell made of an anisotropic, spatially inhomogeneous “transformation medium” that allows rerouting the impinging wave around a given region of space. In its original version, it is generally believed that, in the ideal limit, the radiation cannot penetrate the cloaking shell (from outside to inside, and viceversa). However, it was recently shown by Chen et al. that electromagnetic fields may actually penetrate the cloaked region, provided that this region contains double-negative transformation media which, via proper design, may be in principle used to (partially or totally) “undo” the cloaking transformation, thereby acting as an “anti-cloak.” In this paper, we further elaborate this concept, by considering a more general scenario of cloak/anti-cloak interactions. Our full-wave analytical study provides new insightful results and explores the effects of departure from ideality, suggesting also some novel scenarios for potential applications.