We explore a "partial unification" model that could explain the diphoton
event excess around $750 \, \rm GeV$ recently reported by the LHC experiments.
A new strong gauge group is combined with the ordinary color and hypercharge
gauge groups. The VEV responsible for the combination is of the order of the
$SU(2)\times U(1)$ breaking scale, but the coupling of the new physics to
standard model particles is suppressed by the strong interaction of the new
gauge group. This simple extension of the standard model has a rich
phenomenology, including composite particles of the new confining gauge
interaction, a coloron and a $Z'$ which are rather weakly coupled to standard
model particles, and massive vector bosons charged under both the ordinary
color and hypercharge gauge groups and the new strong gauge group. The new
scalar glueball could have mass of around $750 \, \rm GeV$, be produced by
gluon fusion and decay into two photons, both through loops of the new massive
vector bosons. The simplest version of the model has some issues: the massive
vector bosons are stable and the coloron and the $Z'$ are strongly constrained
by search data. An extension of the model to include additional fermions with
the new gauge coupling, though not as simple and elegant, can address both
issues and more. It allows the massive vector boson to decay into a colorless,
neutral state that could be a candidate of the dark matter. And the coloron and
$Z'$ can decay dominantly into the new fermions, completely changing the search
bounds. In addition, $SU(N)$ fermions below the symmetry breaking scale make it
more plausible that the lightest glueball is at $750$~GeV. Whatever becomes of
the $750$~GeV diphoton excess, the model is an unusual example of how new
physics at small scales could be hidden by strong interactions.