  We study field-induced phase transitions of the minimal exchange model
proposed earlier for BaCo$_2$(AsO$_4$)$_2$, a candidate for Kitaev honeycomb
model, using numerical minimization of classical spin clusters. We show that
experimentally observed sequence of step-like transitions in magnetic field is
realized in the phase diagram of the minimal model. Surprisingly, intermediate
up-up-down plateau phase is stabilized only in the proximity of a
double-zigzag$-$zigzag phase boundary. We systematically map out the region of
stability of experimentally observed cascade of transitions and argue that
BaCo$_2$(AsO$_4$)$_2$ exchange parameters are close to a region of strong phase
competition, which can explain suppressed saturation field.
