  We investigate the effect of Dzyaloshinskii-Moriya (DM) interactions in the
planar pyrochlore (checkerboard) antiferromagnet, one of the paradigmatic
models of spin frustration, and establish the classical phase diagram using a
combination of analytical and numerical approaches. While anisotropic
interactions generally tend to remove the frustration, here we show that a high
degree of frustration survives in a large region of the phase diagram. In
conjunction with the fixed handedness introduced by the DM anisotropy, this
spawns a cascade of incommensurate and double-twisted multi-domain phases,
consisting of spatially intertwined domains of the underlying competing phases
of the isotropic frustrated point. The results underpin a novel mechanism of
generating multi-Q phases in systems that combine high degree of frustration
and chiral interactions.
