  We study the existence of post-Lie algebra structures on pairs of Lie
algebras $(\mathfrak{g},\mathfrak{n})$, where one of the algebras is perfect
non-semisimple, and the other one is abelian, nilpotent non-abelian, solvable
non-nilpotent, simple, semisimple non-simple, reductive non-semisimple or
complete non-perfect. We prove several non-existence results, but also provide
examples in some cases for the existence of a post-Lie algebra structure. Among
other results we show that there is no post-Lie algebra structure on
$(\mathfrak{g},\mathfrak{n})$, where $\mathfrak{g}$ is perfect non-semisimple,
and $\mathfrak{n}$ is $\mathfrak{sl}_3(\mathbb{C})$. We also show that there is
no post-Lie algebra structure on $(\mathfrak{g},\mathfrak{n})$, where
$\mathfrak{g}$ is perfect and $\mathfrak{n}$ is reductive with a
$1$-dimensional center.
