  We have found an unusual competition of two frustration mechanisms in the 2D
quantum antiferromagnet Cs$_2$CoBr$_4$. The key actors are the alternation of
single-ion planar anisotropy direction of the individual magnetic Co$^{2+}$
ions, and their arrangement in a distorted triangular lattice structure. In
particular, the uniquely oriented Ising-type anisotropy emerges from the
competition of easy-plane ones, and for a magnetic field applied along this
axis one finds a cascade of five ordered phases at low temperatures. Two of
these phases feature magnetization plateaux. The low-field one is supposed to
be a consequence of a collinear ground state stabilized by the anisotropy,
while the other plateau bears characteristics of an "up-up-down" state
exclusive for lattices with triangular exchange patterns. Such coexistence of
the magnetization plateaux is a fingerprint of competition between the
anisotropy and the geometric frustration in Cs$_2$CoBr$_4$.
