  Properties of stochastic systems are defined by the noise type and
deterministic forces acting on the system. In out-of-equilibrium setups, e.g.,
for motions under action of L\'evy noises, the existence of the stationary
state is not only determined by the potential but also by the noise. Potential
wells need to be steeper than parabolic in order to assure existence of
stationary states. The existence of stationary states, in sub-harmonic
potential wells, can be restored by stochastic resetting, which is the protocol
of starting over at random times. Herein we demonstrate that the combined
action of L\'evy noise and Poissonian stochastic resetting can result in the
phase transition between non-equilibrium stationary states of various
multimodality in the overdamped system in super-harmonic potentials. Fine-tuned
resetting rates can increase the modality of stationary states, while for high
resetting rates the multimodality is destroyed as the stochastic resetting
limits the spread of particles.
