The massive use of personal location devices, the Internet of Mobile Things, and Location Based Social Networks, enables the collection of vast amounts of movement data. Such data can be enriched with several semantic dimensions (or aspects), i.e., contextual and heterogeneous information captured in the surrounding environment, leading to the creation of multiple aspect trajectories (MATs). In this work, we present how the MAT-Builder system can be used for the semantic enrichment processing of movement data while being agnostic to aspects and external semantic data sources. This is achieved by integrating MAT-Builder into a methodology which encompasses three design principles and a uniform representation formalism for enriched data based on the Resource Description Framework (RDF) format. An example scenario involving the generation and querying of a dataset of MATs gives a glimpse of the possibilities that our methodology can open up.