Accessibility is a key concept in transport and land use policies, and infrastructure-based measures are one important category of accessibility measures. Recently, there has been a significant increase in the attention paid in both academic literature and policy documents to the robustness of the transport system. However, there is not a mature body of literature on the infrastructure-based accessibility measures expressing this concept. This paper proposes a family of accessibility measures to express the robustness of the transport system. These have in common that they express the number of travel options between a given origin and destination, or to conduct activities. The family of measures is conceptualized by using the multi-state supernetwork approach. With respect to the travel options, we discuss (1) the overlap of travel routes, and (2) the choices of travel modes (e.g. car versus train; multimodal). With respect to the activities, we discuss (1) the choice of OD pairs as opposed to activity-travel patterns, and (2) fixed versus flexible activity locations and fixed versus flexible order of activities. We illustrate the travel options and robustness in a multi-modal transport system between the city centers of the Hague-Rotterdam-Dordrecht corridor (The Netherlands).