An M9-partition of a graph is a partition of its vertex set into an independent set and a set inducing a complete bipartite graph, i.e. an M 9 -partition is a 3-coloring ( I, J, K) with the additional restriction that each vertex in part J is adjacent to all vertices in part K. A counipolar partition of a graph is a partition of its vertex set into an independent set and a set inducing a complete multipartite graph. In this work, we present partial results on the structure of the families of P 5 -free graphs admitting either a counipolar or an M9 -partition. Specifically, we focus on forbidden induced subgraph characterizations and recognition algorithms for these graph classes.