Darwin's finches are a classic example of adaptive radiation. The ecological diversity of the Galapagos in part explains that radiation, but the fact that other founder species did not radiate suggests that other factors are also important. One hypothesis attempting to identify the extra factor is the flexible stem hypothesis, connecting individual adaptability to species richness. According to this hypothesis, the ancestral finches were flexible and therefore able to adapt to the new and harsh environment they encountered by exploiting new food types and developing new foraging techniques. Phenotypic variation was initially mediated by learning, but genetic accommodation entrenched differences and supplemented them with morphological adaptations. This process subsequently led to diversification and speciation of the Darwin's finches. Their current behaviour is consistent with this hypothesis as these birds use unusual resources by extraordinary means. In this paper, we identify cognitive capacities on which flexibility and innovation depend. The flexible stem hypothesis predicts that we will find high levels of these capacities in all species of Darwin's finches (not just those using innovative techniques). Here, we test that prediction, and find that while most of our data are in line with the flexible stem hypothesis, some are in tension with it.