  We assess the importance of final state interactions in $D^+ \rar K^- \p^+
\p^+$, stressing the consistency between two- and three-body interactions. The
basic building block in the calculation is a $K\pi$ amplitude based on
unitarized chiral perturbation theory and with parameters determined by a fit
to elastic LASS data. Its analytic extension to the second sheet allows the
determination of two poles, associated with the $\k$ and the $K^*(1430)$, and a
representation of the amplitude based on them is constructed. The problem of
unitarity in the three-body system is formulated in terms of an integral
equation, inspired in the Faddeev formalism, which implements a convolution
between the weak vertex and the final state hadronic interaction. Three
different topologies are considered for the former and, subsequently, the decay
amplitude is expressed as a perturbation series. Each term in this series is
systematically related to the previous one and a re-summation was performed.
Remaining effects owing to single and double rescattering processes were then
added and results compared to FOCUS data. We found that proper three-body
effects are important at threshold and fade away rapidly at higher energies.
  Our model, based on a vector weak vertex, can describe qualitative features
of the modulus of the decay amplitude and agrees well with its phase in the
elastic region.
