One of the phases of information systems design methodologies is that of conceptual schema design. This phase involves identifying relevant objects, their properties and propositions involving these objects. These are described in a conceptual schema using a conceptual schema language. Conceptual schema languages which permit a graphical form are becoming more widely accepted under the motivation of being able to see the data structures that exist. However the semantics are somewhat limited with, for example, few integrity constraints being represented. In this paper we show how conceptual schema languages with a graphical form can be extended to permit a wider class of semantics to be represented.