  A quantum anomalous Hall state with high Chern number has so far been
realized in multiplayer structures consisting of alternating magnetic and
undoped topological insulator layers. However, in previous proposals, the Chern
number can be only tuned by varying the doping concentration or the width of
the magnetic topological insulator layers. This drawback largely restrict the
applications of dissipationless chiral edge currents in electronics since the
number of conducting channels remains fixed. In this work, we propose a way of
varying the Chern number at will in these multilayered structures by means of
an external electric field applied along the stacking direction. In the
presence of an electric field in the stacking direction, the inverted bands of
the unbiased structure coalesce and hybridize, generating new inverted bands
and collapsing the previously inverted ones. In this way, the number of Chern
states can be tuned externally in the sample, without the need of modifying the
number and width of the layers or the doping level. We showed that this effect
can be uncovered by the variation of the transverse conductance as a function
of the electric field at constant injection energy at the Fermi level.
