The widespread adoption of personal location devices, the Internet of Mobile Things, and Location Based Social Networks, enables the collection of vast amounts of movement data. This data often needs to be enriched with a variety of semantic dimensions, or aspects, that provide contextual and heterogeneous information about the surrounding environment, resulting in the creation of multiple aspect trajectories (MATs). Common examples of aspects can be points of interest, user photos, transportation means, weather conditions, social media posts, and many more. However, the literature does not currently provide a consensus on how to semantically enrich mobility data with aspects, particularly in dynamic scenarios where semantic information is extracted from numerous and heterogeneous external data sources. In this work, we aim to address this issue by presenting a comprehensive methodology to facilitate end users in instantiating their semantic enrichment processes of movement data. The methodology is agnostic to semantic aspects and external semantic data sources. The vision behind our methodology rests on three pillars: (1) three design principles which we argue are necessary for designing systems capable of instantiating arbitrary semantic enrichment processes; (2) the MAT-BUILDER system, which embodies these principles; (3) the use of an RDF knowledge graph-based representation to store MATs datasets, thereby enabling uniform querying and analysis of enriched movement data. We qualitatively evaluate the methodology in two complementary example scenarios, where we show both the potential in generating interesting and useful semantically enriched mobility datasets, and the expressive power in querying the resulting RDF trajectories with SPARQL.