In this paper, we consider indirect adaptive pole-placement control (APPC) of linear multivariable stochastic systems, Instead of the canonical representation often used in the literature, we propose using a nomminimal but otherwise uniquely identifiable pseudo canonical parameterization that is more suitable for multivariable ARMAX model identification, To identify the plant, we use the weighted extended least-squares (WELS) algorithm, a least-squares method with slowly decreasing weights which was introduced in [1], The pole-placement controller parameters are then calculated by using a certain perturbation of the parameter estimates such that the linear models corresponding to the perturbed estimates are uniformly controllable and observable, We prove that with a reasonable amount of prior information, the resulting APPC scheme is globally stabilizing and asymptotically self-tuning regardless of the degree of persistency of external excitation, These results represent the most complete study of stochastic multivariable APPC systems to this date.