In this paper, a hierarchical PO-MOESP subspace identification algorithm for directed acyclic graphs (DAGs) is presented. The state of every node and the structure of the graph are assumed to be unknown. The method computes a hierarchical partition of the DAG by using projection matrices typically used in subspace identification methods applied in cascade. Then, the column space of the observability matrix of every node is sequentially estimated by projecting away the input-output data from the previous levels. A past input-output instrumental variable approach is adopted to deal with the noise. The topology of multilevel DAGs is revealed by dedicated projections applied on every level. Moreover, we provide a brief study of a more general class of DAGs that can be accurately represented by multilevel DAGs of reduced interconnection structure. Finally, three simulation examples are provided to show the effectiveness of the proposed methodology.