Nanoshells, classically comprising gold as the metallic component and silica as the dielectric material, are important for fundamental studies in nanoplasmonics. They also empower a myriad of applications, including sensing, energy harvesting, and cancer therapy. Yet, laborious preparation precludes the development of next-generation nanoshells with structural complexity, compositional diversity, and tailorable plasmonic behaviors. This work presents an efficient approach to the bottom-up assembly of concentric nanoshells. By employing polydopamine as the dielectric material and exploiting its intrinsic adhesiveness and pH-tunable surface charge, the growth of each shell only takes 3-4 hours at room temperature. A series of polydopamine-based concentric nanoshells with programmable nanogap thickness, elemental composition (gold and silver), and geometrical configuration (number of layers) is prepared, followed by extensive structural characterization. Four of the silver-containing nanostructures are newly reported. Systematic investigations into the plasmonic properties of concentric nanoshells as a function of their structural parameters further reveal multiple Fano resonances and local-field "hot spots", infrequently reported plasmonic features for individual nanostructures fabricated using bottom-up wet chemistry. These results establish materials design rules for engineering complex plasmon-based systems originating from the integration of multiple plasmonic elements into defined locations within a compact nanostructure.