 Exceptional points, EPS, in open systems non-hermitian physics involve simultaneous coalescence of eigenvalues and eigenstates, which we study in optical micro-disc cavities with concentrically-layered refractive index profiles, showing an EP with two coalescing modes in a double-layered cavity and three coalescing modes in a triple-layered cavity. This article was authored by Julius Kulig, Zhang Huanyi, Martina Henchel, and others.