A generalized version of the scattering transformation is introduced 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.