A generalized version of the scattering transformation is proposed which allows for rendering of the input-output characteristics of a nonlinear conic system into an arbitrary prescribed conic sector. The transformation is consequently applied to the problem of stabilization of conic systems interconnections; the stability is achieved by rendering the input-output characteristics of the subsystems into complementary cones such that the graph separation stability condition is satisfied. In the presence of communication delays, the scattering-based technique for stabilization of feedback interconnections is generalized to the case of arbitrary conic subsystems.