Computational studies using effective potentials that treat water as a rigid molecule were the first to predict the existence of a plastic phase of ice VII. Fifteen years later, this prediction was confirmed experimentally: in the plastic phase, water molecules retain the translational order of the body-centered cubic lattice while undergoing jump-like rotational motion typical of the liquid. Here, we show that this plastic phase also emerges in simulations employing the data-driven many-body MB-pol potential. The phase appears at high pressure, sandwiched between the liquid and ice VII phases. Our results confirm the first-order nature of both the ice VII-plastic and plastic-liquid transitions. Moreover, we find that ice VII exhibits rotational motion of hydrogen atoms on the nanosecond timescale near the melting line, although this motion is qualitatively distinct from that observed in the plastic phase. These results support the existence of the plastic phase beyond rigid-molecule models and provide new insight into the rotational dynamics of ice under extreme conditions.