In this work, we consider a cache-aided network where the users share the end-caches. In particular, a user has access to only one of the caches and the number of caches is less than the number of users. We propose a coded placement scheme that exploits the asymmetry in the number of users associated with each cache. Some of the signals sent to the overloaded caches facilitate the decoding of the coded subfiles stored at the underloaded caches. We present an explicit caching scheme and fully characterize the coded placement gain for two-cache systems. Then, we generalize our scheme to larger networks, where the optimal parameters are characterized by solving a linear program. We observe that, with the proposed scheme, as the asymmetry in the users' connectivity increases, the gain from coded placement is more evident.