We present results of an updated calculation of the two particle two hole (2p2h) contribution to the neutrino-induced charge-current cross section. We provide also some exclusive observables, interesting from the point of view of experimental studies, e.g., distributions of momenta of the outgoing nucleons and of available energy, which we compare with the results obtained within the NEUT generator. We also compute, and separate from the total, the contributions of 3p3h mechanisms. Finally, we discuss the differences between the present results and previous implementations of the model in MC event generators, done at the level of inclusive cross sections, which might significantly influence the experimental analyses, particularly in the cases where the hadronic observables are considered.