  We present a Monte Carlo study of the magnetic properties of an Ising
multilayer ferrimagnet. The system consists of two kinds of non-equivalent
planes, one of which is site-diluted. All intralayer couplings are
ferromagnetic. The different kinds of planes are stacked alternately and the
interlayer couplings are antiferromagnetic. We perform the simulations using
the Wolff algorithm and employ multiple histogram reweighting and finite-size
scaling methods to analyze the data with special emphasis on the study of
compensation phenomena. Compensation and critical temperatures of the system
are obtained as functions of the Hamiltonian parameters and we present a
detailed discussion about the contribution of each parameter to the presence or
absence of the compensation effect. A comparison is presented between our
results and those reported in the literature for the same model using the pair
approximation. We also compare our results with those obtained through both the
pair approximation and Monte Carlo simulations for the bilayer system.
