Belief shadowing is a relatively recent approach to belief change. In essence, shadowing depends on accepting beliefs of others at the expense of dismissing, perhaps temporarily, some of the own ones. As a transient belief change, it is useful when an agent, acting as a group member or playing a particular role, has to adopt adequate "external" beliefs. So far two forms of shadowing, single and multiple, have been considered. While the former specifies shadowing when an agent belongs to a single group or plays a single role, multiple shadowing relaxes this restriction.In the paper we generalize shadowing to arbitrary finitely many-valued logics and consider more complex semantical structures allowing arbitrarily nested sets of worlds. We show that in this general setting multiple shadowing can be represented by single shadowing. The complexity of queries involving such generic shadowing operators is also analyzed.