  Scenarios based on the existence of large or warped (Randall-Sundrum model)
extra dimensions have been proposed for addressing the long standing puzzle of
gauge hierarchy problem. Within the contexts of both those scenarios, a novel
and original type of mechanism generating small (Dirac) neutrino masses, which
relies on the presence of additional right-handed neutrinos that propagate in
the bulk, has arisen. The main objective of the present study is to determine
whether this geometrical mechanism can produce reasonable neutrino masses also
in the interesting multi-brane extensions of the Randall-Sundrum model. We
demonstrate that, in some multi-brane extensions, neutrino masses in agreement
with all relevant experimental bounds can indeed be generated but at the price
of a constraint (stronger than the existing ones) on the bulk geometry, and
that the other multi-brane models even conflict with those experimental bounds.
