  We study localized nonlinear waves on a plane wave background in the multiple
self-induced transparency (SIT) system, which describes an important
enhancement of the amplification and control of optical waves compared to the
single SIT system. A hierarchy of exact multiparametric rational solutions in a
compact determinant representation are presented. We demonstrate that, this
family of solutions contains known rogue wave solution and unusual W-shaped
soliton solution, which strictly corresponds to the linear stability analysis
that involves modulation instability and stability regimes in the low
perturbation frequency region. State transitions between rogue waves and
W-shaped solitons as well as the higher-order nonlinear superposition modes are
revealed by the suitable choice for the background wavenumber of electric field
component. In particular, our results show that, the multiple SIT system admits
stationary and nonstationary nonlinear modes in contrast to the results in the
single SIT system. Correspondingly, the important characteristics of the
nonlinear waves including trajectories and spectrum are revealed in detail.
