The problem of searching large knowledge bases is becoming an important facet of the current web of steadily proliferating semantic content. By pushing the notion of a context for partitioning large knowledge bases, performance of search is improved by narrowing the search space to a context of interest. On the other hand, by restricting the search only to a particular context, some answer can be missed, downgrading the search accuracy. In order to mitigate this drawback, we propose to extend the standard query algorithms with the operation of context shifting, i.e., the operation that allows switching to a close context, if the current context does not contain satisfactory information to answer a query. The paper provides a conceptual description of shifting in contextualized knowledge bases (CKB); and a prototypical implementation of a CKB that supports context shifting. For the conceptual description we adopt and extend the contextas-a-box paradigm introduced in [15]. In such a framework, a context is identified by a set of dimensions, whose values are taken from value-sets structured in hierarchies. Context shifting allows to switch from one context to another by changing the value of one or more dimensions along the corresponding hierarchies. For the prototypical implementation of a CKB we adopt and extend Sesame RDF store in order to support context shifting.