  A microscopic formalism is developed that includes the coupling to two
particle-hole phonons in the particle-hole propagator by extending the dressed
random phase approximation (DRPA) equation for a finite system.
  The resulting formalism is applied to study the low-lying excitation spectrum
of 16O.
  It is observed that the coupling to two-phonon states at low energy generates
excited states with quantum numbers that cannot be obtained in the DRPA
approach.
  Nevertheless, the two-phonon states mix weakly with particle-hole
configurations and participate only partially in the formation of the
lowest-lying positive-parity excited states.
  The stability of the present calculation is tested vs. the truncation of
model space. It is demonstrated that when single-particle strength
fragmentation is properly considered, the present formalism exhibits
convergence with respect to the chosen model space within the confines of the
chosen approximation scheme.
