Unsupervised Domain Adaptation (UDA) aims to transfer a model from a labeled source domain to an unlabeled target domain, addressing challenges of distinct data distributions, termed domain shift. Existing UDA research primarily focuses on classification-like tasks, but neglects ranking and filtering tasks essential for applications like medical diagnosis and search engines. This paper is the first to notice and identify a new real-world transfer problem: cross-stage transfer in multi-stage cascade ranking and filtering systems, a common issue in diverse applications, including information retrieval systems, medical diagnosis, and other real-world ranking/filtering systems. In this problem, we emphasize the crucial assumption of order-invariance and address the key issue named Cross-stage Class Concept Conflict (C4), highlighting potential inconsistencies in class concepts for the same sample at different stages. To tackle these challenges, we propose a novel method, Unsupervised Rank Adaptation (URA), comprising two key components: order-conditional distribution alignment, characterizing the order-conditional distribution intra-stage and aligning them across stages; and principal projection alignment, aligning the principal component’s projection matrix with classifier parameters to ensure order-invariance without guessing pseudo-labels, mitigating the influence of C4. Experimental results show that our approach reaches state-of-the-art performance in various cross-stage transfer tasks.