We study higher-rank generalized Killing tensors with mixed symmetries, providing a couple of examples and applications. It is shown that such objects naturally exist in higher-dimensional rotating black hole spacetimes, where they arise as partially contracted squares of Killing-Yano tensors and display interesting algebraic and differential properties. Motivated by conformal Killing tensors, a generalization of these objects that gives rise to parallel-transported tensors along null geodesics is proposed and shown to exist in higher-dimensional rotating black hole spacetimes.