Roles and positions are structural components in complex social systems which group actors based on how similarly they are connected to the rest of the actors. Role and position detection methods have been successfully used to evaluate and understand the dynamics of social networks and the behavior of their members. However, actor similarities used to detect positions have been based on pairwise comparisons so far: e.g., structural equivalence states that Alice and Bob are in the same position if they are both connected or not to the same other actors in the network, one by one. In this work we present a new framework to find positions and roles using comparisons between actors and sets of actors instead of just using pairwise comparisons. In this way we enable the usage of many more measures of similarity inside position and role detection methods, e.g., based on distances, community structure, triangles and cliques. As a result, we can identify new types of easily interpretable positions. Additionally, the proposed idea can be adapted to more complex models like hypergraphs or multiplex/multi-relational networks. We have evaluated our work on both synthetic and real data, using several existing and new similarity measures and providing both qualitative and quantitative evidence of the new possibilities enabled by our approach.