  We study the incoherent multiple scattering effects on heavy meson production
in the backward rapidity region of p+A collisions within the generalized
high-twist factorization formalism. We calculate explicitly the double
scattering contributions to the heavy meson differential cross sections by
taking into account both initial-state and final-state interactions, and find
that these corrections are positive. We further evaluate the nuclear
modification factor for muons that come form the semi-leptonic decays of heavy
flavor mesons. Phenomenological applications in d+Au collisions at a
center-of-mass energy $\sqrt{s}=200$ GeV at RHIC and in p+Pb collisions at
$\sqrt{s}=5.02$ TeV at the LHC are presented. We find that incoherent multiple
scattering can describe rather well the observed nuclear enhancement in the
intermediate $p_T$ region for such reactions.
