  In this paper we analyze the scattering process in a two-field model in
$(1+1)$-dimensions, with the special property to have several topological
solutions: i) one with higher rest mass, characterized by a nested defect (lump
inside a kink), and ii) four others having lower rest mass, degenerated, and
characterized by a kink inside kink. We investigate kink-antikink symmetric
scattering, where the kink and antikink have higher rest mass and the same
initial velocity modulus $v$. The output of scattering presents a wide range of
behaviors, such as annihilation of the kink-antikink pair, the emission of
radiation jets, the generation of oscillating pulses and the change of the
topological sector. We show that the changing of the topological sector is
favored, and only two of the four sectors are possible as outcomes. Moreover,
despite the degeneracy in energy, the distribution of the final states is
asymmetric in the phase space, being an effect of the presence of vibrational
states.
