The highly frustrated rare-earth-based magnet Nd₃BWO₉ is a promising candidate in the search for proximate spin-liquid physics. We present a thorough investigation on single crystals of this material using bulk and microscopic techniques. Magnetization data reveal a fractional magnetization plateau for three different investigated field directions. The magnetic phase diagram is mapped out from calorimetric data and exhibits several domes of magnetic order below 0.3 K. Propagation vectors for all ordered phases are presented. The results suggest complex ordering in this material, and unveil the existence of a commensuration transition of the propagation vector at zero magnetic field. A scenario where interplane exchange interactions are essential to a magnetic model of Nd₃BWO₉ is discussed.