Product service systems (PSS) can be understood as an innovation/business strategy that includes a set of products and services that are realized by an actor network. More recently, PSS that comprise System of Systems (SoS) have been of increasing interest, notably in the transportation (autonomous vehicle infrastructures, multi-modal transportation) and energy sector (smart grids). Architecting such PSS-SoS goes beyond classic SoS engineering, as they are often driven by new technology, without an a priori client and actor network, and thus, a much larger number of potential architectures. However, it seems that neither the existing PSS nor SoS literature provides solutions to how to architect such PSS. This paper presents a methodology for architecting PSS-SoS that are driven by technological innovation. The objective is to design PSS-SoS architectures together with their value proposition and business model from an initial technology impact assessment. For this purpose, we adapt approaches from the strategic management, business modeling, PSS and SoS architecting literature. We illustrate the methodology by applying it to the case of an automobile PSS.