In this study, we propose such sequential tuning methods of multivariable optimal regulators that can be applied to the tuning of control systems under operation. In such tuning, it is desirable to change feedback gains only step by step, confirming that the control performance is actually improved in each step. The first method we propose is such that we design an optimal single-input regulator in each step, by paying attention to only one input of the plant while the feedback laws to other inputs are fixed to those obtained in the previous sequential tuning steps. On the other hand, the second method is such that all elements of the feedback gain are changed at once, while we are given the design freedom about how much we are to change the gain. These two methods as well as their combined use are shown to lead to the optimal gain as a multivariable control system eventually, provided that the sequential tuning steps are repeated sufficiently many times. We apply these methods to the tuning of LQI servo systems, and carry out the simulation study of the control of a hot strip mill to illustrate the tuning law and show its effectiveness.