  The Cu-$3d$ states in the high-$T_c$ cuprates are often described as a single
band of $3d_{x^2-y^2}$ states, with the other four $3d$ states having about 2
to 3 eV higher energy due to the lower-than-octahedral crystal field at the
copper sites. However, excitations to these higher energy states observed with
RIXS show indications of strong coupling to doped holes in the $3d_{x^2-y^2}$
band. This relaunches a decades-old question of the possible role of the
orbital degrees of freedom that once motivated Bednorz and M\"uller to search
for superconductivity in these systems. Here we explore a direction different
from the Jahn-Teller electron-phonon coupling considered by Bednorz and
M\"uller, namely the interaction between holes mediated by $dd$ excitations.
