Developing products and services concurrently bears great potential as well as challenges. Systems Engineering (SE) is an interdisciplinary approach, which aims to enable the realization of successful systems. Model-based systems engineering (MBSE) is a SE approach focusing on the utilization of models for information exchange instead of documents. Methods and tools for MBSE are advanced and effective. Nevertheless, the field predominantly focuses on technical systems rather than on services and business models. In the context of the increasing importance of the Service Economy and rising innovative business models, an extension of the MBSE methods and tools to a service- and business model-centric view constitutes a research gap. Sufficient methods for requirements definition in PSS design have been developed. In concept design, the outline or rough concept of the product is defined. This step is currently not supported with useful methods. In order to address this research gap, the authors have proposed Integrated Product Service Architectures (IPSSAs) in previous research, which depict physical product architectures and service architectures in one integrated model. In previous studies, Systems Modelling Language (SysML) was identified as suitable modelling notations for IPSSAs, but several drawbacks of the notation were noted. Within this paper, a study is presented, which identifies suitable combinations of modelling notations and diagrams for IPSSA modelling. The combination of several diagrams from SysML, Business Process Modelling Notation (BPMN) and Data Flow Architecture is used on the practical example of ELSA (Engineering Living Systems of Autonomy), a service robot for guest and plant care. In order to address the lack of process-based service modelling in SysML, BPMN is added to common SysML modelling. In order address the data flow dimension, a third modelling notation, the Data Flow Architecture is proposed.