  The quest for exotic quantum magnetic ground states, including the Kitaev
spin liquid and quantum spin-ices, has led to the discovery of several quantum
materials where low energy pseudospin-$1/2$ doublets arise from the splitting
of spin-orbit entangled multiplets with higher degeneracy. Such systems include
$d$-orbital and $f$-orbital Mott insulators. When the gap between the low
energy pseudospin-$1/2$ levels and the excited levels of the multiplet or
`excitons' is not large, the effective low-energy exchange interactions between
the low energy pseudospin-$1/2$ moments can acquire significant corrections
from coupling to the excitons. We extract these corrections using higher order
perturbation theory as well as an exact Schrieffer-Wolff transformation. Such
corrections can impact the exchange matrix for the low energy pseudospin-$1/2$
levels by renormalizing the strength and the sign of Heisenberg exchange or
Ising anisotropies, and potentially even inducing bond-anisotropic couplings
such as Kitaev-$\Gamma$ exchange interactions. We discuss recent experiments on
various cobaltate and osmate materials which hint at the ubiquity and
importance of this physics.
