  Nearly all 6D superconformal field theories (SCFTs) have a partial tensor
branch description in terms of a generalized quiver gauge theory consisting of
a long one-dimensional spine of quiver nodes with links given by conformal
matter; a strongly coupled generalization of a bifundamental hypermultiplet.
For theories obtained from M5-branes probing an ADE singularity, this was
recently leveraged to extract a protected large R-charge subsector of
operators, with operator mixing controlled at leading order in an inverse large
R-charge expansion by an integrable spin $s$ Heisenberg spin chain, where $s$
is determined by the $\mathfrak{su}(2)_{R}$ R-symmetry representation of the
conformal matter operator. In this work, we show that this same structure
extends to the full superconformal algebra $\mathfrak{osp}(6,2|1)$. In
particular, we determine the corresponding Bethe ansatz equations which govern
this super-spin chain, as well as distinguished subsectors which close under
operator mixing. Similar considerations extend to 6D little string theories
(LSTs) and 4D $\mathcal{N} = 2$ SCFTs with the same generalized quiver
structures.
