This contribution about amplitude analyses in multibody hadronic charm decays deals with some attempts to introduce theoretical constraints.
Different effective hadronic formalism approaches are mentioned.
A recent work, based on a basic weak interaction process and a Chiral unitary model to account for the final state interaction, is described in details for the $f_0(980)$ production in $D_s^+ \to \pi^+ \pi^+ \pi^-$ and $D_s^+ \to \pi^+ K^+ K^- $ decays.
Within the framework of the diagrammatic approach and flavor symmetry, a global analysis of two-body $D$ decays into a vector meson and a pseudoscalar meson is presented.
A quasi-two-body QCD factorization model for $D$ decays into three mesons and its recent application to $D^0 \to K_S^0 \pi^+ \pi^-$ is outlined.
For processes with final-state pions and kaons and as an alternative to the sum of Breit-Wigner amplitudes, often used in experimental Dalitz-plot analyses,
amplitude parametrizations, in term of unitary $\pi \pi$, $\pi K$ and $K \bar K$ form factors, are proposed.
These parametrizations are derived from quasi-two-body factorization models.