We propose a scheme to generate spin cat states, i.e., superpositions of maximally separated quasiclassical states on a single high-dimensional nuclear spin in a solid-state device. We exploit a strong quadrupolar nonlinearity to drive the nucleus significantly faster than usual gate sequences, achieving collapses and revivals two orders of magnitude faster than the dephasing timescale. Furthermore, these states are engineered without entanglement with an ancilla, hence, are robust against error propagation. With our multitone control, we can realize arbitrary high-spin rotations within an experimentally feasible regime, as well as transform a spin coherent state to a spin cat state using only phase modulation, opening the possibility of storing and manipulating high-fidelity cat states.