Via the adjunction −· 1 ⊣ \( \mathcal V \)(1,−) : Span(\( \mathcal V \)) → \( \mathcal V \)-Mat and a cartesian monad T on an extensive category \( \mathcal V \) with finite limits, we construct an adjunction −·1 ⊣ \( \mathcal V \)(1,−) : Cat(T, \( \mathcal V \)) → (T, \( \mathcal V \))-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, the left adjoint is fully faithful, and preserves pullbacks, provided that − · 1: Set → \( \mathcal V \) 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.