  We exhibit Anosov subgroups of $\mathsf{SL}_d(\mathbb{R})$ that do not embed
discretely in any rank-$1$ simple Lie group of noncompact type, or indeed, in
any finite product of such Lie groups. These subgroups are isomorphic to free
products $\Gamma * \Delta$, where $\Gamma$ is a uniform lattice in
$\mathsf{F}_4^{(-20)}$ and $\Delta$ is a uniform lattice in $\mathsf{Sp}(m,1)$,
$m \geq 51$.
