In this paper, we consider modal multilattices with Tarski, Kuratowski, and Halmos closure and interior operators as well as the corresponding logics which are multilattice versions of the modal logics MNT4, S4, and S5, respectively. The former modal multilattice logic is a new one. The latter two modal multilattice logics have been already mentioned in the literature, but algebraic completeness results have not been established for them before. We present a multilattice version of MNT4 in a form of a sequent calculus and prove the algebraic and neighbourhood completeness theorems for it. We extend the algebraic completeness result for the multilattice versions of S4 and S5 as well
