  We derive the inclusive breakup cross section of a three-fragment projectile
nuclei, $a = b +x_1 + x_2$, in the spectator model. The resulting four-body
cross section for observing $b$, is composed of the elastic breakup cross
section which contains information about the correlation between the two
participant fragments, and the inclusive non-elastic breakup cross section.
This latter cross section is found to be a non-trivial four-body generalization
of the Austern formula \cite{Austern1987}, which is proportional to a matrix
element of the form, $\langle\hat{\rho}_{{x_1},{x_2}}\left|\left[W_{{x_1}} +
W_{{x_2}} + W_{3B}\right]\right|\hat{\rho}_{{x_1}, {x_2}}\rangle$. The new
feature here is the three-body absorption, represented by the imaginary
potential, $W_{3B}$. We analyze this type of absorption and supply ideas of how
to calculate its contribution.
