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Strong geometrical frustration in magnets leads to exotic states such as spin liquids, spin supersolids, and complex magnetic textures. SrCu₂(BO₃)₂, a spin-1/2 Heisenberg antiferromagnet in the archetypical Shastry–Sutherland lattice, exhibits a rich spectrum of magnetization plateaus and stripe-like magnetic textures in applied fields. The structure of these plateaus is still highly controversial due to the intrinsic complexity associated with frustration and competing length scales. We discover magnetic textures in SrCu₂(BO₃)₂ via magnetostriction and magnetocaloric measurements in fields up to 100.75 T. In addition to observing low-field fine structure with unprecedented resolution, the data also reveal lattice responses at 73.6 T and at 82 T that we attribute, using a controlled density matrix renormalization group approach, to a unanticipated 2/5 plateau and to the long-predicted 1/2 plateau.