  Perturbative methods are attractive to describe the electronic structure of
molecular systems because of their low-computational cost and systematically
improvable character. In this work, a two-step perturbative approach is
introduced combining multi-state Rayleigh-Schr\"odinger (effective Hamiltonian
theory) and state-specific Brillouin-Wigner schemes to treat degenerate
configurations and yield an efficient evaluation of multiple energies. The
first step produces model functions and an updated definition of the
perturbative partitioning of the Hamiltonian. The second step inherits the
improved starting point provided in the first step, enabling then faster
processing of the perturbative corrections for each individual state. The
here-proposed two-step method is exemplified on a model-Hamiltonian of
increasing complexity.
