An explicit closed form determination of the inverse dielectric function for an N-sheet two-dimensional (2D) electron superlattice embedded in a nonlocal bulk host semiconductor plasma is presented here, as well as for an infinite superlattice. The coupled plasmon dispersion relation is analyzed for the model in which the 2D quantum wells constituting the superlattice have just one occupied subband and the bulk plasma of the host has hydrodynamic nonlocality. Nonlocal corrections are obtained for a hybrid superlattice plasmon in interaction with the host bulk plasmon. In addition, we find that this model predicts a new nonlocal low-frequency mode.