Language models often exhibit undesirable behaviors, such as gender bias or toxic language. Interventions in the representation space were shown effective in mitigating such issues by altering the LM behavior. We first show that two prominent intervention techniques, Linear Erasure and Steering Vectors, do not enable a high degree of control and are limited in expressivity. We then propose a novel intervention methodology for generating expressive counterfactuals in the representation space, aiming to make representations of a source class (e.g., "toxic'') resemble those of a target class (e.g., "non-toxic''). This approach, generalizing previous linear intervention techniques, utilizes a closed-form solution for the Earth Mover's problem under Gaussian assumptions and provides theoretical guarantees on the representation space's geometric organization. We further build on this technique and derive a nonlinear intervention that enables controlled generation. We demonstrate the effectiveness of the proposed approaches in mitigating bias in multiclass classification and in reducing the generation of toxic language, outperforming strong baselines.