Where do emergent features come from? This has long been an intriging puzzle. The concept of pet fish illustrates the difficulty. Most people expect pet fish to live in bowls, even though this is not something either pets or fish normally do. The inference that pet fish have the feature of living in bowls cannot be explained purely in terms of the constituents themselves. The feature seems to emerge. The present paper aims to explain this effect using notions of classificatory composition. Adjoined concept references are taken to construct classifications rather than combinations; a pet fish is taken to be a fish classified as a pet rather than a combination of a pet a fish. It is also shown that, where concepts have a compositional representation, feature emergence can be accounted for in terms of compositional accommodation.