  We derive a master equation for a superradiant medium which includes
multilevel interference betwen the individual scatterers. The derivation relies
on the Born-Markov approximation and implements the coarse graining formalism.
The master equation fulfils the Lindblad form and contains terms describing
single-atom multilevel interference, multi-atom interference between identical
transitions, and multi-atom interference between different electronic
transitions with parallel dipoles. This formalism is then applied to determine
the excitation spectrum of two emitters using the parameters of the Hydrogen
transitions 2S$_{1/2}\,\to$4P$_{1/2}$ and 2S$_{1/2}\,\to$4P$_{3/2}$, where the
gap between the parallel dipoles is of the order of GHz. The distortion of the
signal due to the interplay of multilevel and multi-emitter interference is
analysed as a function of their distance. These results suggest that
interference between parallel dipolar transition can significantly affect the
spectroscopic properties of optically dense media.
