Nonparametric estimates of frequency response functions (FRFs) are often suitable for describing the dynamics of a mechanical system. If treating these estimates as measurements, they can be used for parametric identification of, e.g., a gray-box model. This paper shows that a more accurate parametric model can be identified based on local parametric FRF estimates, giving a shorter total experiment time, compared to classical methods. Classical methods for nonparametric FRF estimation of MIMO (Multiple Input Multiple Output) systems require at least as many experiments as the system has inputs. Local parametric FRF estimation methods have been developed for avoiding multiple experiments. In this paper, these local methods are adapted and applied for estimating the FRFs of a 6-axes robotic manipulator, which is a nonlinear MIMO system operating in closed loop. The aim is to reduce the experiment time and amount of data needed for identification. The resulting FRFs are analyzed in an experimental study and compared to estimates obtained by classical MIMO techniques.