  This paper studies a \emph{packing} problem in the so-called beyond-planar
setting, that is when the host graph is ``almost-planar'' in some sense.
Precisely, we consider the case that the host graph is $k$-planar, i.e., it
admits an embedding with at most $k$ crossings per edge, and focus on families
of $\Delta$-regular caterpillars, that are caterpillars whose non-leaf vertices
have the same degree $\Delta$. We study the dependency of $k$ from the number
$h$ of caterpillars that are packed, both in the case that these caterpillars
are all isomorphic to one another (in which case the packing is called
\emph{placement}) and when they are not. We give necessary and sufficient
conditions for the placement of $h$ $\Delta$-regular caterpillars and
sufficient conditions for the packing of a set of $\Delta_1$-, $\Delta_2$-,
$\dots$, $\Delta_h$-regular caterpillars such that the degree $\Delta_i$ and
the degree $\Delta_j$ of the non-leaf vertices can differ from one caterpillar
to another, for $1 \leq i,j \leq h$, $i\neq j$.
