  This study deals with a piecewise $\phi^2$ scalar field theory in $(1+1)$
dimensions. The scalar field potential is designed with a triple-well shape,
engendering kink solutions with asymmetric square-well linearized potentials.
Thus, the localized and delocalized modes in this model can be obtained
analytically in terms of transcendental equations. This allows us to explore
kink-antikink and antikink-kink collisions with any desired number of localized
and delocalized modes. We obtain new scenarios of resonance windows
suppression, shedding light on the role of higher excited modes in kink
scattering.
