  We provide a Sandwich Theorem (K\"onig (1972)) for positively homogeneous
functionals that satisfy additivity only on a restricted domain. Our relaxation
of additivity is based on a binary relation called convex-conic symmetric
preorder, whereby additivity is restricted to all couples of elements that
belong to such relation. We then study applications of our nonlinear Sandwich
Theorem, proving extension and envelope representation results. Finally, we
consider some applications to comonotonicity, a key property in decision
theory, risk measurement, and the theory of risk sharing.
