TOSCANA is a computer program which allows an online interaction with data bases to analyse and explore data conceptually. Such interaction uses conceptual data systems which are based on formal contexts consisting of relationships between objects and attributes. Those formal contexts often have attributes taken from a thesaurus, which may be understood as ordered set and be completed to a join-semilattice (if necessary). The join of thesaurus terms indicates the degree of resemblance of the terms and should therefore be included in the formal contexts containing those terms. Consequently, the formal contexts of a conceptual data system based on a thesaurus should have join-closed attribute sets. A problem arises for the TOSCANA-system implementing such conceptual data system because the attributes in a nested line diagram produced by TOSCANA might not be join-closed, although its components have join-closed attribute sets. In this paper we offer a solution to this problem by developing a method for extending line diagrams to those whose attributes are join-closed. This method allows to implement TOSCANA-systems based on thesauri which respect the join-structure of the thesauri.