  We prove the existence of higher-order topological insulators with protected
chiral hinge modes in quasi-two-dimensional systems made out of coupled layers
stacked in an inversion-symmetric manner. In particular, we show that an
external magnetic field drives a stack of alternating p- and n-doped buckled
honeycomb layers into a higher-order topological phase, characterized by a
non-trivial three-dimensional ${\mathbb Z}_2$ invariant. We identify silicene
multilayers as a potential material platform for the experimental detection of
this novel topological insulating phase.
