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We report ultrasound velocity measurements carried out on single crystals of UPt₃, in magnetic fields, B, applied at various angles between c-axis and the basal plane. For B||c-axis, θ=90^o, we observe magneto-acoustic oscillations that commence at fields as low as 12T. These oscillations suddenly break into a very large amplitude at 24.8 T implying a Lifshitz transition. Continuing to higher fields these large amplitude oscillations disappear at 30 T beyond which much smaller oscillations with altered frequencies are observed. Magnetostriction measurements performed at fields up to 65 T for θ=90^o reveal small features that are consistent with boundaries at similar magnetic field values. Further, the 30 T transition appears to merge with the angle dependent metamagnetic transition at the intermediate angle θ=50^o. For field along this unique angle the magnetostriction along c-axis vanishes precisely for all magnetic field values. High resolution magnetization measurements vs. field are, surprisingly, featureless and near linear when θ=90^o.