  We construct polarized Calabi--Yau 3-folds with at worst isolated canonical
orbifold points in codimension 4 that can be described in terms of the
equations of the Segre embedding of $\mathbb P^2 \times \mathbb P^2$ in
$\mathbb P^8$. We investigate the existence of other deformation families in
their Hilbert scheme by either studying Tom and Jerry degenerations or by
comparing their Hilbert series with those of existing low codimension
Calabi--Yau 3-folds. Among other interesting results, we find a family of
Calabi--Yau 3-fold with five distinct Tom and Jerry deformation families, a
phenomenon not seen for $\mathbb Q$-Fano 3-folds. We compute the Hodge numbers
of $\mathbb P^2 \times \mathbb P^2 $ Calabi--Yau 3-folds and corresponding
manifolds obtained by performing crepant resolutions. We obtain a manifold with
a pair of Hodge numbers that does not appear in the famously known list of
30108 distinct Hodge pairs of Kruzer--Skarke, in the list of 7890 distinct
Hodge pairs corresponding to complete intersections in the product of
projective spaces and in Hodge paris obtained from Calabi--Yau 3-folds having
low codimension embeddings in weighted projective spaces.
