  Momenta of charmonia created in Pb-Pb collisions at the Large Hadron Collider
are so large that three or more mesons may be produced when the charmonia
collide with light mesons in hadronic matter. We study the meson-charmonium
collision in a mechanism where the collision produces two quarks and two
antiquarks, the charm quark then fragmenting into charmed mesons, and the other
three constituents as well as quarks and antiquarks created from vacuum give
rise to two or more mesons. The absolute square of the transition amplitude for
the production of two quarks and two antiquarks is derived from the $S$-matrix
element, and cross-section formulas are derived from the absolute square of the
transition amplitude and charm-quark fragmentation functions. With a
temperature-dependent quark potential, we calculate unpolarized cross sections
for inclusive $D^+$, $D^0$, $D^+_s$, or $D^{*+}$ production in scattering of
charmonia by $\pi$, $\rho$, $K$, or $K^\ast$ mesons. At low center-of-mass
energies of the charmonium and the light meson, the cross sections are very
small. At high energies the cross sections have obvious temperature dependence,
and are comparable to peak cross sections of two-to-two meson-charmonium
reactions.
