We discuss the potential of multilayered plasmonic particles to tailor the optical scattering response. The interplay of plasmons localized in thin stacked shells realizes peculiar degenerate cloaking and resonant states occurring at arbitrarily close frequencies. These concepts are applied to realize ultrasharp comblike scattering responses and synthesize staggered, ideally strong superscattering states closely coupled to invisible states. We demonstrate robustness to material losses and to variations in the background medium, properties that make these structures ideal for optical tagging.