A two-step interaction scheme involving ⁽²⁾ and ⁽³⁾ nonlinear media is suggested for the generation of Schrödinger cat-like states of a single-mode optical field. In the first step, a weak coherent signal undergoes a self-Kerr phase modulation in a ⁽³⁾ crystal, leading to a Kerr kitten, namely a microscopic superposition of two coherent states with opposite phases. In the second step, such a Kerr kitten enters a ⁽²⁾ crystal and, in turn, plays the role of a quantum seed for stimulated phase-sensitive amplification. The output state in the above-threshold regime consists in a quantum superposition of mesoscopically distinguishable squeezed states, i.e. an optical cat-like state. The whole setup does not rely on conditional measurements, and is robust against decoherence, as only weak signals interact with the Kerr medium.