Rotating a nonspherical object introduces rich and surprising dynamics to a classical mechanics problem. It has been shown that a rolling ellipse in air can rock, roll, or jump along a flat surface. Even for a rolling sphere, deformability can significantly alter its mobility compared to a rigid counterpart. Here, we experimentally examine both transitions between motion modes and the role of deformability using a driven ellipsoid that can be either rigid or soft. Using a geometric framework, we successfully model the motion of the rigid ellipsoid and identify the critical angular velocity for the rolling-to-jumping transition. Since shape strongly influences motion modes, we further explore the role of deformability using a soft ellipsoid. By modifying the soft ellipsoid’s shape, we tune the rolling-to-jumping transition in situ, and observe that soft ellipsoids move more efficiently along ramps than their rigid counterparts.