The importance of similarity search has become prominent in the fast-evolving vector databases, which apply content embedding techniques on complex data to produce and manage large collections of high-dimensional vectors. Processing of such data is only possible by using a similarity function for storage, structure, and retrieval. However, if multiple users access the collection, their views on similarity can differ as similarity, in general, is subjective and context-dependent. In this article, we elaborate on the problem of a similarity search engine implementation, where users use a common index but search with personalised views of similarity, implemented by a possibly different similarity model. Specifically, we define a foundational theoretical framework and conduct experiments on real-life data to confirm the viability of such an approach. The experiments also indicate future research directions needed to propose and implement an effective and efficient personalised similarity search engine.