The newly discovered Nd${}_{3}$BWO${}_{9}$ is a rare instance of a disorder-free magnet with an exchange topology interpolating between 2D kagome and 1D spin tubes. In this study, an array of measurements reveals its exotic phase diagram. The complex frustration mechanism results in several ordered phases, including two different, typically two-dimensional 1/3- magnetization plateaux. Meanwhile, one-dimensional tube correlations are unequivocally identified by signatures in both thermodynamic and microscopic probes.