Humans have the remarkable ability to learn new categories from few examples, but how few examples can we actually learn from? Recent studies suggest it may be possible to learn more novel concepts than the number of examples. Previous approaches to such less-than-one-shot (LO-shot) learning used soft labels to provide weighted mappings from each example to multiple categories. Unfortunately, people find soft labels unintuitive and this approach did not provide plausible, cognitively-grounded mechanisms for LO-shot learning at scale. We propose a new paradigm that leverages well-established learning strategies: reducing complex stimuli to primitives, learning by discrimination, and generalizing to novel compositions of features. We show that participants can learn 22 categories from just 4 examples, shedding light on the mechanisms involved in LO-shot learning. Our results provide valuable insights into the human ability to learn many categories from limited examples, and the strategies people employ to achieve this impressive feat.