  We study the quasiparticle spectrum in an underscreened Kondo-lattice (KL)
model that involves a single spin degenerate conduction band and two
crystalline-electric-field (CEF) split Kramers doublets coupled by both
orbital-diagonal and non-diagonal exchange interactions. We find the three
quasiparticle bands of the model using a constrained fermionic mean field
approach. While two bands are similar to the one-orbital model a new genuinely
heavy band inside the main hybridization gap appears in the quasiquartet model.
Its dispersion is due to effective hybridization with conduction states but the
bandwidth is controled by the size of the CEF splitting. Furthermore several
new indirect and direct hybridztion gaps may be identified. By solving the
selfconsistency equation we calculate the CEF- splitting and exchange
dependence of effective Kondo low energy scale, hybridization gaps and band
widths. We also derive the quasiparticle spectral densities and their partial
orbital contributions. We suggest that the two-orbital KL model can exhibit
mixed CEF/Kondo excitonic magnetism.
