In recent years, unfalsified adaptive switching supervisory control (UASSC) has emerged as an effective technique for tackling the problem of controlling uncertain plants only on the basis of the plant I/O data. The aim of this paper is to construct a novel switching logic, which, when combined with appropriate test functions, makes it possible to extend UASSC, so far restricted to time-invariant systems, to the case of systems whose dynamics are subject to infrequent but possibly large variations.