In the existing unsupervised domain adaptation (UDA) methods for remote sensing images (RSIs) semantic segmentation, class symmetry is an widely followed ideal assumption, where the source and target RSIs have exactly the same class space. In practice, however, it is often very difficult to find a source RSI with exactly the same classes as the target RSI. More commonly, there are multiple source RSIs available. To this end, a novel class asymmetry RSIs domain adaptation method with multiple sources is proposed in this paper, which consists of four key components. Firstly, a multi-branch segmentation network is built to learn an expert for each source RSI. Secondly, a novel collaborative learning method with the cross-domain mixing strategy is proposed, to supplement the class information for each source while achieving the domain adaptation of each source-target pair. Thirdly, a pseudo-label generation strategy is proposed to effectively combine strengths of different experts, which can be flexibly applied to two cases where the source class union is equal to or includes the target class set. Fourthly, a multiview-enhanced knowledge integration module is developed for the high-level knowledge routing and transfer from multiple domains to target predictions.