  A structure $\mathcal{M}$ in a first-order language $\mathcal{L}$ is
\emph{indivisible} if for every coloring of $M$ in two colors, there is a
monochromatic $\mathcal{M}^{\prime} \subseteq \mathcal{M}$ such that
$\mathcal{M}^{\prime}\cong\mathcal{M}$. Additionally, we say that $\mathcal{M}$
is symmetrically indivisible if $\mathcal{M}^{\prime}$ can be chosen to be
\emph{symmetrically embedded} in $\mathcal{M}$ (that is, every automorphism of
$\mathcal{M}^{\prime}$ can be extended to an automorphism of $\mathcal{M}$). In
the following paper we give a general method for constructing new symmetrically
indivisible structures out of existing ones. Using this method, we construct
$2^{\aleph_0}$ many non-isomorphic symmetrically indivisible countable
structures in given (elementary) classes and answer negatively the following
question asked by A. Hasson, M. Kojman and A. Onshuus in "On symmetric
indivisibility of countable structures" (Cont. Math. 558(1):453--466): Let
$\mathcal{M}$ be a symmetrically indivisible structure in a language
$\mathcal{L}$. Let $\mathcal{L}_0 \subseteq \mathcal{L}$. Is $ \mathcal{M}
\upharpoonright \mathcal{L}_0$ symmetrically indivisible?
