When scholars extend their models and hypotheses to encompass additional cases, they may need to adapt their concepts to fit new contexts. Giovanni Sartori’s work on conceptual traveling and conceptual stretching provides helpful guidance in addressing this fundamental task. Sartori’s framework draws on what may be called a classical understanding of conceptual hierarchies. Each successive concept as one moves down the hierarchy is a “kind of” in relation to the one above it – such that it may be called a kind hierarchy. Concepts have clear boundaries and defining properties shared by all cases deemed to fit the concept. This chapter examines the challenge to this framework presented by two nonclassical approaches: Wittgenstein’s family resemblances and Lakoff’s radial structures. According to these alternative perspectives, concepts may not be sharply bounded, and some attributes may not be shared by all cases viewed as corresponding to the concept. Because they only partly correspond to the concept, this may be called a part–whole hierarchy. With such patterns, strict application of a classical framework can lead to abandoning concepts prematurely or modifying them inappropriately. This chapter discusses solutions to these problems, suggesting that these two forms of hierarchy can productively be used together.