Caching popular content at the edge of future mobile networks has been widely considered in order to alleviate the impact of the data tsunami on both the access and backhaul networks. A number of interesting techniques have been proposed, including femto-caching and "delayed" or opportunistic cache access. Nevertheless, the majority of these approaches suffer from the rather limited storage capacity of the edge caches, compared to the tremendous and rapidly increasing size of the Internet content catalog. We propose to depart from the assumption of hard cache misses, common in most existing works, and consider "soft" cache misses, where if the original content is not available, an alternative content that is locally cached can be recommended. Given that Internet content consumption is increasingly entertainment-oriented, we believe that a related content could often lead to complete or at least partial user satisfaction, without the need to retrieve the original content over expensive links. In this paper, we formulate the problem of optimal edge caching with soft cache hits, in the context of delayed access, and analyze the expected gains. We then show using synthetic and real datasets of related video contents that promising caching gains could be achieved in practice.