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In the dairy industry, maintaining the welfare of every cow and curbing financial losses requires individual-level surveillance, which is achieved through cow Re-Identification (Re-ID). Computer vision-based Re-ID hinges on visually distinguishing characteristics, such as the specific coat patterns seen in breeds like Holstein. However, manually labelling every cow across all farms is financially unfeasible. We aim to formulate Re-ID strategies that work on both annotated and non-annotated farms, accommodating new individuals and varied settings. Unsupervised Domain Adaptation (UDA) approaches aim to close this divide by transferring knowledge from labelled source domains to unlabelled target domains. However, they have largely been tailored to person and vehicle Re-ID scenarios. Our research proposes Cumulative Unsupervised Multi-Domain Adaptation (CUMDA) to address the challenges of constrained identity variation and dissimilar farm appearances. CUMDA gathers knowledge across all domains, reinforcing specialization in familiar domains while strengthening generalization to unknown ones. Our offerings include a CUMDA technique that adapts to multiple unlabelled target domains while safeguarding source-domain efficacy, along with thorough cross-dataset testing across three cattle Re-ID datasets. These tests reveal substantial gains in source conservation, target-domain specialization, and adaptation to unseen domains.