Model-based multivariable control requires good-quality process models which, in addition to standard specifications for model quality, must also satisfy certain control-relevant conditions to allow for robust closed-loop operation. In recent work, we developed a rigorous mathematical framework for practical design of experiments that produce models satisfying the integral controllability condition for nxn systems. In this work we extend our framework, which previously employed a static description of the identified plant, to the dynamic case for multivariable finite impulse response (FIR) models. The extended mathematical framework directly suggests a methodology for experiment design that incorporates integral controllability, and satisfies maximum variance constraints on each input and output variable. We perform simulations on an industrial 5x5 model to demonstrate the effectiveness of the approach and compare it to previous results in literature.