We discuss the photoproduction of a photon-meson pair in the collinear factorisation framework as a channel for the extraction of GPDs. What makes this channel interesting, from among the family of $2 \to 3$ processes, is that depending on the chosen meson (and its polarisation) in the final state, one is able to probe chiral-even and chiral-odd GPDs, as well as gluonic GPDs, all at the leading twist. More specifically, we consider the case where the outgoing meson is a pion or rho meson (with any charge). In fact, choosing a transversely-polarised rho meson in the final state allows us to access chiral-odd quark GPDs at the leading twist, which are not known experimentally. Working at leading order in QCD, we compute the cross sections and polarisation asymmetries (wrt the incoming photon) for the various final state mesons, and we discuss the prospects of measuring them at various experiments, namely JLab-12, COMPASS, future EIC, and ultra-peripheral collisions at LHC.