  We discuss the exclusive photoproduction of a photon-meson pair with large $
p_{T} $ as a channel to probe generalised parton distributions (GPDs). Like
other $ 2\to3 $ exclusive processes, this channel allows us to better study the
$ x $-dependence of GPDs, in contrast to $ 2\to2 $ processes such as Deeply
Virtual Compton Scattering (DVCS) which give only "moment-type" information.
Moreover, it also gives the possibility to access, at leading twist, the
chiral-odd GPDs, which are still completely unknown experimentally. In the
first part of these proceedings, we present the computation of the amplitude at
leading order and leading twist, for charged pions, and rho mesons of any
charge and polarisation. These processes are sensitive to quark GPDs only. We
also discuss the possibility of measuring such processes at various
experiments, namely JLab, COMPASS, future EIC and LHC in ultra-peripheral
collisions. In particular, in collider experiments, the dependence of GPDs at
small skewness $ (<10^{-3}) $ can be extracted. For the second part, we report
on our recent work on the exclusive photoproduction of $ \pi^{0}\gamma $ pair,
which, in addition to a quark GPD channel, also has a contribution from gluon
GPDs. In the latter case, we demonstrate that a collinear factorisation of the
process fails, due to the presence of a Glauber pinch. Our findings also imply
that other similar processes, like $ \pi ^{0} N \to \gamma \gamma N $ also
suffer from the same issue. On the other hand, we stress that the processes
discussed earlier, which are sensitive to the quark GPD channels only, are safe
from these factorisation breaking effects.
