In this work we address multi-target domain adaptation (MTDA) in semantic segmentation, which consists in adapting a single model from an annotated source dataset to multiple unannotated target datasets that differ in their underlying data distributions. To address MTDA, we propose a self-training strategy that employs pseudo-labels to induce cooperation among multiple domain-specific classifiers. We employ feature stylization as an efficient way to generate image views that forms an integral part of self-training. Additionally, to prevent the network from overfitting to noisy pseudo-labels, we devise a rectification strategy that leverages the predictions from different classifiers to estimate the quality of pseudo-labels. Our extensive experiments on numerous settings, based on four different semantic segmentation datasets, validate the effectiveness of the proposed self-training strategy and show that our method outperforms state-of-the-art MTDA approaches. Code available at: https://github.com/Mael-zys/CoaST