  Among the simple Lie algebras, $D_4$ is distinguished as the unique one whose
group of outer-automorphisms is bigger than $\mathbb{Z}_2$. We study the
compactifications of the $D_4$ (2,0) Theory on a punctured Riemann surface,
$C$, with outer-automorphism twists around cycles of $C$ lying in
$\mathbb{Z}_3\subset \text{Aut}(D_4)= S_3$. The resulting 4D $\mathcal{N}=2$
SCFTs have a number of new and interesting properties. As byproduct, we
discover a new rank-1 $\mathcal{N}=2$ SCFT with flavour symmetry group $SU(4)$.
