A novel approach to the energy conversion aspect of multi-energy system modelling is presented. Derived from the Energy Hubs modelling concept, a framework is proposed which can account for conversion topologies of arbitrary complexity. In particular, no constraint is placed upon the direction of energy flow through a given system and subsequently, terminals of the conversion model can serve as both inputs and outputs. Binary decision variables with mutual exclusivity constraints effectively allow the energy conversion topology to be re-configured to its optimal form, for a given set of system conditions. The proposed approach is systematic and amenable to software implementation as an entire conversion model can be described by a single connection matrix with associated index set. The power and flexibility of the approach is exemplified by way of a case study and associated numerical results. The paper is concluded by discussing future work related to the proposed modelling approach.