  We extend a recent result that for the (additive) semigroup of positive
integers $\mathbb{N}$, there are continuum many subdirect products of
$\mathbb{N} \times \mathbb{N}$ up to isomorphism. We prove that for $U,V$ each
one of $\mathbb{Z}$ (the group of integers), $\mathbb{N}_{0}$ (the monoid of
non-negative integers), or $\mathbb{N}$, we prove that $U \times V$ has
continuum many (semigroup) subdirect products up to isomorphism.
