A group is called W*-superrigid if its group von Neumann algebra completely remembers the original group. In this talk I will present a joint work with Stefaan Vaes in which we generalize W*-superrigidity for groups in two directions. Firstly, we find a class of groups for which W*-superrigidity holds in the presence of a twist by an arbitrary 2-cocyle: the twisted group von Neumann algebra completely remembers both the original group and the 2-cocycle. Secondly, for the same class of groups, the superrigidity also holds up to virtual isomorphism. If time permits, I will moreover explain how this result and the technical machinery behind it led to other new W*-superrigidity theorems in two different contexts.