A 0-1 matrix M is saturating for a 0-1 matrix P if M does not contain a submatrix that can be turned into P by flipping any number of its 1-entries to 0-entries, and flipping any 0-entry of M to 1-entry introduces a copy of P . Matrix M is semisaturating for P if flipping any 0-entry of M to 1-entry introduces a new copy of P , regardless of whether M originally contains P or not. The functions ex(n; P ) and sat(n; P ) are the maximum and minimum possible number of 1-entries a n n 0-1 matrix saturating for P can have, respectively. The function ssat(n; P ) is the minimum possible number of 1-entries an n n 0-1 matrix semisaturating for P can have. The function ex(n; P ) has been studied for decades, while investigation on sat(n; P ) and ssat(n; P ) was initiated recently. In this paper, a nontrivial generalization of results regarding these functions to multidimensional 0-1 matrices is made. In particular, the exact values of ex(n; P; d) and sat(n; P; d) are found when P is a d-dimensional identity matrix. Finally, a necessary and sufficient condition for a multidimensional 0-1 matrix to have a bounded semisaturation function is given.