Multiple ionization (MI), induced by a few EUV photons at energies of 28.2 eV, 38 eV and 44 eV from FLASH (the free-electron laser at Hamburg), has been studied for atoms (He, Ne, Ar) and N2 molecules utilizing our multi-hit coincident technology—the reaction microscope. At comparably low intensities of I 1011–1013 W cm−2 we find the non-sequential (NS) MI mechanism dominating Ar3+ and Ar4+ production. Inspecting recoil ion and electron momentum distributions evidence is provided (i) for preferential back-to-back emission of electrons for NS double ionization of He and (ii) for angular entanglement between two outgoing electrons in sequential ionization (SI). In contrast to atoms, SI is observed to be most effective for MI of N2 molecules at an intensity of ~1013 W cm−2 leading, among others, to N2+2 → N+ + N+, N3+2 → N2+ + N+, N4+2 → N2+ + N2+ Coulomb explosion channels. Fragment ion momentum distributions are investigated and are demonstrated to allow tracing SI pathways.