Mechanism design over social networks, whose goal is to incentivize agents to diffuse the information of a mechanism to their followers, as well as to report their true preferences, is one of the new trends in market design. In this paper, we reconsider the traditional house allocation problem with existing tenants from the perspective of mechanism design over social networks. Since our model is a generalization of the networked housing market investigated by Kawasaki et al. , no mechanism simultaneously satisfies strategy-proofness, individual rationality and Pareto efficiency for general social network structures. We therefore examine the cases where the social network has a tree structure. We first show that even for the restricted structure, a weaker welfare requirement called non-wastefulness is not achievable by any strategy-proof and individually rational mechanism. We then show that a non-trivial modification of You Request My House - I Get Your Turn mechanism (YRMH-IGYT) is individually rational, strategy-proof, and weakly non-wasteful. Furthermore, it chooses an allocation in the strict core for neighbors and satisfies weak group strategy-proofness.