We consider stochastic discrete-time systems with multiplicative noise which are controlled by dynamic output feedback and subjected to blockdiagonal stochastic parameter perturbations. Stability radii for these systems are characterized via scaling techniques and it is shown that for real data, the real and the complex stability radii coincide. In a second part of the paper we investigate the problem of maximizing the stability radii by dynamic output feedback. Necessary and sufficient conditions are derived for the existence of a stabilizing compensator which ensures that the stability radius is above a prespecified level. These conditions consist of parametrized matrix inequalities and a coupling condition.