  We study a class of multistate Landau-Zener model which cannot be solved by
integrability conditions or other standard techniques. By analyzing analytical
constraints on its scattering matrix and performing fitting to results from
numerical simulations of the Schr\"{o}dinger equation, we find nearly exact
analytical expressions of all its transition probabilities for specific
parameter choices. We also determine the transition probabilities up to leading
orders of series expansions in terms of the inverse sweep rate (namely, in the
diabatic limit) for general parameter choices. We further show that this model
can describe a Su-Schrieffer-Heeger chain with couplings changing linearly in
time. Our work presents a new route, i.e., analytical constraint plus fitting,
to analyze those multistate Landau-Zener models which are beyond the
applicability of conventional solving methods.
