The purpose of this paper is to shed light on the concept of MaaS and what characterises a ‘MaaS service’, as well as to propose a topology of MaaS as a tool for facilitating the discussion of MaaS, enabling the ‘comparison of’ different services, understanding MaaS' potential effects, and aiding the integration of societal goals into MaaS services. Based on an exploration of existing definitions and descriptions of MaaS, and an expert workshop identifying key aspects and ascertaining service differentiations accordingly, the resulting proposed topology consists of MaaS Levels 0 to 4 as characterised by different types of integration: 0 no integration; 1 integration of information; 2 integration of booking and payment; 3 integration of the service offer, including contracts and responsibilities; 4 integration of societal goals. The levels are then described in terms of their added value and further discussed regarding implications for society, business, users/customers, and technical requirements. Then, a deeper discussion also delves into the potential in expanding upon Level 4 and ways by which services and societal goals can become more fully integrated. The proposed topology adds clarity to the discussion of such a trending topic and enables the positioning of services along the MaaS spectrum. It also deepens the understanding of why MaaS can take time to establish, and can help support the development of action plans in terms of what needs to be done depending on what type of MaaS one wants to develop. Further analysis is desirable regarding the possibilities and problems linked with the different levels of MaaS. Such an analysis is key to understanding which effects can be achieved via the implementation of different levels of MaaS services in terms of e.g. social, economic and ecological sustainability, and business potential.