Iterative feedback tuning is a model free control tuning method using closed loop experiments. For single-input single-output systems only 2 or 3, depending on the controller structure, closed loop experiments are required. However for multivariable systems the number of experiments increases to a maximum of 1 + m × p, where m × p is the dimension of the controller. In this contribution several methods are proposed to reduce the experimental time by approximating the gradient of the cost function. The local convergence for a method which uses the same technique as in IFT for SISO systems is analyzed. It is shown that even if there are commutation errors due to the approximation method, the numerical optimization may still converge to the true optimum.