In conventional programming, variables can be of more than just base types, they can be of custom types which involve more complex class-like structures. Does the concept programming metaphor preserve this property?
A concept might consist in the relation between two concepts, but that would still be a base concept, except for its weird skew so that it facilitates the mapping between the two during some defined addition or join. A set of concepts might help specify a conceptual framework, so perhaps a set or list or tuple of concepts might be a sensible addition. Custom types are less easy to justify, as a set of concepts would inevitably find themselves in a certain interrelation pattern and hence lack the need for additional context provided through fields of more abstract entities.
This design choice picks up on an important disanalogy between conventional programming and concept programming. In conventional programming, variables are not implicitly related other than e.g. through a specified chain of operations. In concept programming, concepts are implicitly related through their interrelations, likely expressible as ops on distributions over semantic space.