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$_4$.
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