The goal of the present work is to use the canonical rMC simulations to explore the role of electrostatic correlations in CR in suspensions containing multivalent ions. We will demonstrate that a modified mean-field theory is able to correctly account for the CR in suspensions containing multivalent coions -showing that electrostatic correlations are only marginally important in such systems. On the other hand, for systems with multivalent counterions, the mean-field theory fails dramatically, demonstrating that electrostatic correlations are of fundamental importance for CR in suspensions with multivalent counterions.