  Semileptonic three-body $D \to A\ell^+\nu_\ell$ decays, nonleptonic $A \to
VP$ decays and semileptonic four-body $D \to A(A \to VP)\ell^+\nu_\ell$ strong
or electromagnetic decays are analyzed by the SU(3) flavor symmetry/breaking
approach, where $A$ denotes the axial-vector meson, $V$ denotes the vector
meson, and $P$ denotes pseudoscalar meson. In terms of the SU(3) flavor
symmetry/breaking, the decay amplitudes of the $D \to A \ell^+ \nu_\ell$ decays
or the vertex coefficients of the $A \to VP$ decays are related. The relevant
nonperturbative parameters are constrained by the present experimental data.
Then the branching ratios of the $D \to A \ell^+ \nu_\ell $, $A \to VP$ and
$D\to A(A\to VP)\ell^+\nu_\ell$ decays are predicted by the constrained
parameters. We find that some branching ratios are large and they might be
measured in the near future experiments. Moreover, the sensitivities of the
branching ratios of $D \to A \ell^+ \nu_\ell $ and $A \to VP$ decays to the
parameters are also shown, and some decay branching ratios are sensitive to the
nonperturbative parameters.
