The paper presents a two-phase methodological protocol for creating an Extended Matrix (EM) based BIM model (EM-BIM). The EM, developed by the ISPC-CNR institute, was designed to manage data, metadata, and paradata related to virtual reconstructions in archaeology. This research introduces a methodology for geometric and informational modelling, based on an HBIM approach, of existing architectural heritage using EM tools within Historical Building Information Modelling (HBIM) approach. Knowledge-based structure of EM is similar to object-based system of BIM: both methodologies are grounded in a relational approach to 3D data structuring. Furthermore, EM explicitly incorporates paradata using a visual knowledge graph system. Tested on the Doric Stoa of Priene, the first phase of the study focused on decoding the graphic language of EM to automatically generate and populate ad hoc descriptors within the HBIM environment using a visual programming language (VPL). A second phase involved the setting up of a BuildingSMART Data Dictionary (bsDD) to map the EM classification against the IFC classes, to standardise the generation of dedicated ‘property sets’.