  We present results of the updated SuperChic 3 Monte Carlo event generator for
central exclusive production. This extends the previous treatment of
proton-proton collisions to include heavy ion (pA and AA) beams, for both
photon and QCD-initiated production, the first time such a unified treatment of
exclusive processes has been presented in a single generator. To achieve this
we have developed a theory of the gap survival factor in heavy ion collisions,
which allows us to derive some straightforward results about the $A$ scaling of
the corresponding cross sections. We compare against the recent ATLAS and CMS
measurements of light-by-light scattering at the LHC, in lead-lead collisions.
We find that the background from QCD-initiated production is expected to be
very small, in contrast to some earlier estimates. We also present results from
new photon-initiated processes that can now be generated, namely the production
of axion-like particles, monopole pairs and monopolium, top quark pair
production, and the inclusion of $W$ loops in light-by-light scattering.
