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Obtaining sufficient labelled data for model training is impractical for most real-life applications. Therefore, we address the problem of domain generalization for semantic segmentation tasks to reduce the need to acquire and label additional data. Recent work on domain generalization increase data diversity by varying domain-variant features such as colour, style and texture in images. However, excessive stylization or even uniform stylization may reduce performance. Performance reduction is especially pronounced for pixels from minority classes, which are already more challenging to classify compared to pixels from majority classes. Therefore, we introduce a module, $ASH_{+}$, that modulates stylization strength for each pixel depending on the pixel's semantic content. In this work, we also introduce a parameter that balances the element-wise and channel-wise proportion of stylized features with the original source domain features in the stylized source domain images. This learned parameter replaces an empirically determined global hyperparameter, allowing for more fine-grained control over the output stylized image. We conduct multiple experiments to validate the effectiveness of our proposed method. Finally, we evaluate our model on the publicly available benchmark semantic segmentation datasets (Cityscapes and SYNTHIA). Quantitative and qualitative comparisons indicate that our approach is competitive with state-of-the-art. Code is made available at \url{