Multicritical phase transitions in multiply rotating black holes

We show that multi-critical points in which more than three phases coalesce are present multiply rotating Kerr-AdS black holes $d$-dimensions. explicitly a quadruple point for triply hole $d=8$ and quintuple quadruply $d=10$. The maximal number of distinct $n$ is one larger the independent rotations, we outline method obtaining associated $n$-tuple point. Situations also exist where merge at sub-maximal points. Our results thermodynamics common previously thought, with systems potentially supporting many as long sufficient thermodynamic variables present.