[en] In this paper, we study the Cabibbo favored three body non-leptonic $D^{+}\to <!--\; ???\; -->K^{-<!--\; ???\; -->}{\mathrm{\pi <!--\; ??\; -->}}^{+}{\mathrm{\pi <!--\; ??\; -->}}^{+}$ decay. We show that the corresponding direct charge parity (CP) asymmetry is extremely tiny in the framework of the Standard Model (SM) and is out of experimental range. Motivated by this result we extend the study of the CP asymmetries to include a generic model where the CPV weak phase equals ${20}^{\circ <!--\; ???\; -->}$ in a₂, a model with extra gauge bosons within left–right (LR) grand unification models and a model with a charged Higgs boson. We show that the generic model can strongly enhance CP asymmetries—reaching up to 30% in some regions of the Dalitz plots and still being compatible with the existing experimental limit on the total CP asymmetry in this channel. Large CP asymmetries can be achieved in the non-manifest LR models where partial CP asymmetries up to a few $\mathrm{\%<!--\; \%\; -->}$ can be reached and the experimental limit on the total CP asymmetry already can be used to constraint these LR SM extensions. For the two Higgs doublets models the CP asymmetries are of order 10⁻³. (paper)