  Via the adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal V(1,-) \colon
\mathsf{Span}(\mathcal V) \to \mathcal V \text{-} \mathsf{Mat} $ and a
cartesian monad $ T $ on an extensive category $ \mathcal V $ with finite
limits, we construct an adjunction $ - \boldsymbol{\cdot} 1 \dashv \mathcal
V(1,-) \colon \mathsf{Cat}(T,\mathcal V) \to (\overline T, \mathcal
V)\text{-}\mathsf{Cat} $ between categories of generalized enriched
multicategories and generalized internal multicategories, provided the monad $
T $ satisfies a suitable condition, which is satisfied by several examples.
  We verify, moreover, that the left adjoint is fully faithful, and preserves
pullbacks, provided that the copower functor $ - \boldsymbol{\cdot} 1 \colon
\mathsf{Set} \to \mathcal V $ is fully faithful. We also apply this result to
study descent theory of generalized enriched multicategorical structures.
  These results are built upon the study of base-change for generalized
multicategories, which, in turn, was carried out in the context of categories
of horizontal lax algebras arising out of a monad in a suitable 2-category of
pseudodouble categories.
