One key driver of the Linked Data paradigm is the ability to lift data graphs from legacy systems by employing various adapters and RDFizers (e.g., D2RQ for relational databases, XLWrap for spreadsheets). Such approaches aim towards removing boundaries of enterprise data silos by opening them to cross-organizational linking within a "Web of Data". An insufficiently tapped source of machine-readable semantics is the underlying graph nature of diagrammatic conceptual models - a kind of information that is richer compared to what is typically lifted from table schemata, especially when a domain-specific modeling language is employed. The paper advocates an approach to Linked Data enrichment based on a diagrammatic model RDFizer originally developed in the context of the ComVantage FP7 research project. A minimal but illustrative example is provided from which arguments will be generalized, leading to a proposed vision of "conceptual model"-aware information systems.