Learning control methods enable significant performance improvements for systems that operate repetitively. Typical methods rely on a parametric plant model to achieve fast and robust convergence. The aim of this paper is to develop a framework for multivariable systems that enables fast and robust learning without requiring a parametric plant model. This is achieved by connecting nonparametric frequency response function identification and robust control, which enables synthesis on a frequency-by-frequency basis. A nonconservative approach is obtained by ensuring that the identified uncertainty is directly compatible with the developed synthesis framework. Application to a multivariable benchmark motion system confirms the potential of the developed framework.