Cross-talk, where data signatures of different physical properties are confused, is a major concern in multi-parameter FWI. This can be mitigated by using a good estimate of the Newton update in the inversion procedure, but such an approach is typically too computationally intensive to be pursued. In this report, the cost of approximating the Newton update is reduced by considering a multi-resolution approach, in which the grid defining the model is varied with frequency. This approach allows for a smaller computational burden at low frequencies, and effectively mitigates the cost of approximating the Newton update. This allows for cross-talk to be more effectively prevented.