We study (pseudo-)differential operators on a manifold with edge Z,locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y. The typical operators A are coer degenerate in a specific way. They (σψ (A), σ∧ (A), σ∧ (A)), where σψ is the interior symbol and σ∧ (A)(y, η), (y, η) ∈ T*Y,weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind.We show the continuity of coer-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.