We use holography to study the spectrum of multi-twist operators, within conformal field theories in d>2, in the large spin limit. Focusing on a CFT with a global U(1) current, we explore its phase diagram as a function of the U(1) charge Q and angular momentum J, particularly at large J and Q. For states with Q=2, the spectrum is universally described by the long-distance limit of holographic theories, independent of the CFT's specific holographic nature. We extend this analysis to states with Q>2, computing corrections to the energies of Q scalar particles coming from single photon, graviton and scalar exchange in the bulk of AdS. Additionally, we explore the extension of these results to the regime of parametrically large charge Q and discuss the potential universality of these results beyond holographic CFTs, specifically in the context of the the O(2) model in 3d.