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Although there are numerous websites that provide recommendation services for various items such as movies, music, and books, most of studies on recommender systems only focus on one specific item type. As recommender sites expand to cover several types of items, though, it is important to build a hybrid web recommender system that can handle multiple types of items. The switch hybrid recommender model provides a solution to this problem by choosing an appropriate recommender system according to given selection criteria, thereby facilitating cross-domain recommendations supported by individual recommender systems. This paper seeks to answer the question of how to deal with situations where no appropriate recommender system exists to deal with a required type of item. In such cases, the switch model cannot generate recommendation results, leading to the need for a fallback model that can satisfy most users most of the time. Our fallback model exploits a graph-based proximity search, ranking every entity on the graph according to a given proximity measure. We study how to incorporate the fallback model into the switch model, and propose a general architecture and simple algorithms for implementing these ideas. Finally, we present the results of our research result and discuss remaining challenges and possibilities for future research.