A multiparty session forms a unit of structured communication among many participants which follow communication sequences specified as a global type. When a process is engaged in two or more sessions simultaneously, different sessions can be interleaved and can interfere at runtime. Previous work on multiparty session types has ignored session interleaving, providing a limited progress property ensured only within a single session, by assuming non-interference among different sessions and by forbidding delegation. This paper develops, besides a more traditional, compositional communication type system, a novel static interaction type system for global progress in dynamically interleaved and interfered multiparty sessions. The interaction type system infers causalities of channels making sure that processes do not get stuck at intermediate stages of sessions also in presence of delegation.