Developing new techniques at the interface of geometric group theory and von Neumann algebras, we identify the first examples of ICC groups $G$ whose von Neumann algebras are McDuff and exhibit a new rigidity phenomenon, termed McDuff superrigidity: any arbitrary group $H$ satisfying $LG\cong LH$ must decomposes as $H=G \times A$ for some ICC amenable group $A$.  Our groups appear as infinite direct sums of $W^*$-superrigid wreath-like product groups with bounded cocycle.  In this talk I will introduce this class of groups and a natural array into a weakly-$\ell^2$ representation of the group that witnesses the bound on the 2-cocycle. I will then show how this array leads to an interplay between two deformations of the group von Neumann algebra and how these can be used to prove this class of groups satisfies infinite product rigidity.  This is joint work with Ionut Chifan, Denis Osin and Bin Sun.