We put forward a powerful technique that allows generating quasi-non-diffracting light beams with a variety of complex transverse shapes and topologies. We show that, e.g., spi-raling patterns, patterns featuring curved or bent bright stripes, or patterns featuring arbi-trary combinations of harmonic, Bessel, Mathieu and parabolic beams occupying different domains in the transverse plane can be produced. The quasi-non-diffracting patterns open up a wealth of opportunities for the manipulation of matter and optical waves, colloidal and living particles, with applications in biophysics, and quantum, nonlinear and atom optics.