  We investigated non-linear sigma models with cosets G/H represented by
$SU(N)\times SU(N)/SU(N)$, $SU(N)/SO(N)$, and $SU(2N)/USp(2N)$. These models
exhibit a transition to a strongly coupled regime above a threshold energy
scale $\Lambda^*$, where the effective field theory approach breaks down. To
address this issue, we introduced the so called Higgs radial modes within the
Linear Sigma Model, crucial for restoring perturbative unitarity. Analyzing the
$N>2$ case, we first notice that all radial modes coming from the most general
irreducible representation of G are necessary for unitarizing scattering
amplitudes and ensuring the weakly coupled nature of the theory. The
phenomenology behind these extra radial modes recalls the physics of the Higgs
in the electroweak sector of the Standard Model. In the case of a model
describing electroweak symmetry breaking with a more complex pattern, despite
strict constraints from electroweak precision tests, these modes could
stabilize the Higgs potential and be a possible solution for the vacuum
instability issue.
