I feel it would be fun to make the diagrams into category theoretical ologs, which naturally represent relational schemas. You could implement multiple databases, or just one. A functor from an Olog to a value category is a database instance. Natural transforms between instances are migrations.
You can even model exotic dbs, like probabilistic dbs, algebraic dbs, and ontologies.
Not actually sure about how ready for prime time this kind of idea is. I mainly use ologs to sketch schemas and migrations. It might be a huge scary scope creep to pick up categories just to draw some ERD diagrams. But they might inspire your underlying data structures, and how you adapt them to different DBMSs.