Hybrid nanostructures that couple plasmon and exciton resonances generate hybridized energy states, called plexcitons, which may result in unusual light-matter interactions. We report the formation of a transparency dip in the visible spectra of colloidal suspensions containing silver nanoplatelets and a cyanine dye, 1,1′-diethyl-2,2′-cyanine iodide (PIC). PIC was electrostatically adsorbed onto the surface of silver nanoplatelet core particles, forming an outer J-aggregate shell. This core−shell architecture provided a framework for coupling the plasmon resonance of the silver nanoplatelet core with the exciton resonance of the J-aggregate shell. The sizes and aspect ratios of the silver nanoplatelets were controlled to ensure the overlap of the plasmon and exciton resonances. As a measure of the plasmon-exciton coupling strength in the system, the experimentally observed transparency dips correspond to a Rabi splitting energy of 207 meV, among the highest reported for colloidal nanoparticles. The optical properties of the silver platelet-J-aggregate nanocomposites were supported numerically and analytically by the boundary-element method and temporal coupled-mode theory, respectively. Our theoretical predictions and experimental results confirm the presence of a transparency dip for the silver nanoplatelet core Jaggregate shell structures. Additionally, the numerical and analytical calculations indicate that the observed transparencies are dominated by the coupling of absorptive resonances, as opposed to the coupling of scattering resonances. Hence, we describe the suppressed extinction in this study as an induced transparency rather than a Fano resonance.