In a recent paper [1] the concept of "cyclic switching" was proposed as a means of dealing with the well-known stabilizability problem, which arises in adaptive controller synthesis because of the existence of points in parameter space where the design model upon which certainty equivalence control is based loses stabilizability. While the procedure outlined in [1] is specific enough to enable one to construct cyclicly switched adaptive controllers for SISO process models, for the MIMO case two key issues are left unresolved. The objective of this paper is to address both of these issues, thereby extending excitation-free, identifier-based adaptive control methods to minimum and nonminimum phase MIMO linear systems.