  In this paper we analyze the associated production of a vector meson with a
(pseudo)scalar bound state or a dimuon system in ultraperipheral $PbPb$
collisions through the double scattering mechanism for the energies of the
Large Hadron Collider (LHC) and Future Circular Collider (FCC). Our results
complement previous studies for the double vector meson production. We present
our predictions for the total cross sections and rapidity distributions
considering the rapidity ranges covered by the ALICE and LHCb detectors, which
indicate that a future experimental analysis of the $\phi + \eta_c$, $\phi +
\mu^+ \mu^-$ and $J/\Psi + \mu^+ \mu^-$ final states is feasible.
