An analysis of the variance of the parameters of a multi-input plant estimated in closed-loop operation is performed. More specifically, the effect of the simultaneous excitation of an additional input on the variance of the estimated parameters is investigated. The resulting expressions are valid for all conventional Prediction Error Models (PEM). It is shown that, regardless of the parametrization, the presence of an additional reference signal never impairs and, in most cases, improves the accuracy of the parameter estimates. The analytical results are illustrated by two simulation examples.