When multiple datasets describe complementary information about the same set of entities, for example, brain scans of an individual over time, global trade network across years, or user information across social media platforms, integrating these snapshots allows us to see a more holistic picture. A common way of identifying structure in data is through clustering, but while clustering may be applied to each dataset separately, we learn more in the multi-view setting by identifying joint clusters. We consider a clustering problem where each view conflates some of these joint clusters, only revealing partial information, and seek to recover the true joint cluster structure. We introduce this multi-view clustering model and a method for recovering it: the transposed Khatri-RAo Framework for joinT cluster recoverY (KRAFTY). The model is flexible and can accommodate a variety of data-generating processes, including latent positions in random dot product graphs and Gaussian mixtures. A key advantage of KRAFTY is that it represents joint clusters in a space with sufficient dimension so that each joint cluster occupies an orthogonal subspace in the transposed Khatri-Rao matrix, which results in a sharp drop in the scree plot at the true number of joint clusters, enabling easy model selection. Our simulations show that when the number of joint clusters exceeds the sum of the numbers of clusters in each individual view, our method outperforms existing methods in both joint clustering accuracy and estimation of the number of joint clusters.