Recent intense effort has been devoted to exploring different manifestations of resonant excitations of strongly coupled plasmons and excitons, but so far such studies have been limited to situations where the Fano- or Rabi-type spectra are largely symmetric at zero detuning. Using a newly developed full quantum mechanical model, here we reveal the existence of a highly asymmetric spectroscopic regime for both the Rabi splitting and transparency dip. The asymmetric nature is inherently tied to the non-negligible exciton absorbance and is caused by substantial interference-induced energy repartitioning of the resonance peaks. This theoretical framework can be exploited to reveal the quantum behaviors of the two excitation entities with varying mutual coupling strengths in both linear and nonlinear regimes. We also use prototypical systems of rhodamine molecules strongly coupled with AuAg alloyed nanoparticles and well-devised control experiments to demonstrate the validity and tunability of the energy repartitioning and correlated electronic state occupations, as captured by the variations in the asymmetric spectroscopy and corresponding nonlinear absorption coefficient as a function of the Au:Ag ratio. The present study helps to substantially enrich our microscopic understanding of strongly coupled plasmon-exciton systems.