  We explore a variant of the $\phi^6$ model originally proposed in Phys.\
Rev.\ D {\bf 12}, 1606 (1975) as a prototypical, so-called, "bag" model in
which domain walls play the role of quarks within hadrons. We examine the
steady state of the model, namely an apparent bound state of two kink
structures. We explore its linearization, and we find that, as a function of a
parameter controlling the curvature of the potential, an {\it effectively
arbitrary} number of internal modes may arise in the point spectrum of the
linearization about the domain wall profile. We explore some of the key
characteristics of kink-antikink collisions, such as the critical velocity and
the multi-bounce windows, and how they depend on the principal parameter of the
model. We find that the critical velocity exhibits a non-monotonic dependence
on the parameter controlling the curvature of the potential. For the
multi-bounce windows, we find that their range and complexity decrease as the
relevant parameter decreases (and as the number of internal modes in the model
increases). We use a modified collective coordinates method [in the spirit of
recent works such as {Phys.\ Rev.\ D} {\bf 94}, 085008 (2016)] in order to
capture the relevant phenomenology in a semi-analytical manner.
