Motivated by the problem of understanding multi-twist operators in general CFTs, I will discuss the interacting spectrum of large-spin three-particle states in AdS. In particular, I will explain how thanks to the AdS curvature this particular limit of the three-body problem is tractable. The large spin limit effectively becomes a semiclassical limit of a Berezin-Toeplitz Hamiltonian, which allows us to analyze the leading-twist spectrum analytically. Work in progress with Jeremy Mann.