  A generalised orbifold of a defect TQFT $\mathcal{Z}$ is another TQFT
$\mathcal{Z}_{\mathcal{A}}$ obtained by performing a state sum construction
internal to $\mathcal{Z}$. As an input it needs a so-called orbifold datum
$\mathcal{A}$ which is used to label stratifications coming from duals of
triangulations and is subject to conditions encoding the invariance under
Pachner moves. In this paper we extend the construction of generalised
orbifolds of $3$-dimensional TQFTs to include line defects. The result is a
TQFT acting on 3-bordisms with embedded ribbon graphs labelled by a ribbon
category $\mathcal{W}_{\mathcal{A}}$ that we canonically associate to
$\mathcal{Z}$ and $\mathcal{A}$. We also show that for special orbifold data,
the internal state sum construction can be performed on more general skeletons
than those dual to triangulations. This makes computations with
$\mathcal{Z}_{\mathcal{A}}$ easier to handle in specific examples.
