  Multiple field-induced plateaus in $\alpha$-CoV$_2$O$_6$ at low temperatures
were revealed earlier by M. Lenertz et al. [J. Phys. Chem. C 115, 17190 (2011)]
and carefully investigated recently by M. Nandi and P. Mandal [J. Appl. Phys.
119, 133904 (2016)]. Four equidistant steps were observed in the magnetization
curve. We present a model to describe this phenomenon. A magnetic structure of
this substance is formed by highly anisotropic triangular lattice of Ising
chains running along the $\bf{b}$ axis. Due to a three-fold degeneracy of
three-sublattice magnetic ordering, domain boundaries appear. Their
transformation under magnetic field variation leads to two additional steps in
the 1/3 magnetization plateau and gives rise to complex magnetic behavior
observed experimentally. The domain structure in $\alpha$-CoV$_2$O$_6$ occurs
to be strongly anisotropic because a lifetime of the metastable states depends
greatly on the configuration orientation. A strong dependence of the
magnetization curve on magnetic field sweep time is predicted.
