  For a decade and a half, CeCoIn$_5$ and related alloys have served as a rich
playground to explore the interplay between magnetism and unconventional
superconductivity. Despite this extended study, the presence/absence of
metamagnetism (MM) in this ternary system remains as an unresolved issue. Here
we show that the linear and non-linear magnetic response in CeMIn$_5$ (M = Rh,
Ir and Co) can be understood within the context of the recently proposed single
energy scale (SES) model of MM. New measurements of the third-order
susceptibility, $\chi_3$, in CeCoIn$_5$ are presented and together with the
known systematics of the linear susceptibility in all three compounds, are
shown to be consistent with the SES model. Predictions are made for the MM
critical field in CeCoIn$_5$ and the fifth-order susceptibility, $\chi_5$.
