As e-commerce platforms develop different business lines, a special but challenging product categorization scenario emerges, where there are multiple domain-specific category taxonomies and each of them evolves dynamically over time. In order to unify the categorization process and ensure efficiency, we propose a two-stage taxonomy-agnostic framework that relies solely on calculating the semantic relatedness between product titles and category names in the vector space. To further enhance domain transferability and better exploit cross-domain data, we design two plug-in modules: a heuristic mapping scorer and a pretrained contrastive ranking module with the help of meta concepts, which represent keyword knowledge shared across domains. Comprehensive offline experiments show that our method outperforms strong baselineson three dynamic multi-domain product categorization (DMPC) tasks,and online experiments reconfirm its efficacy with a5% increase on seasonal purchase revenue. Related datasets will be released.