  The investigation of macroscopic quantum phenomena is a current active area
of research that offers significant promise to advance the forefronts of both
fundamental and applied quantum science. Utilizing the exquisite precision and
control of quantum optics provides a powerful toolset for generating such
quantum states where the types and 'size' of the states that can be generated
are set by the resourcefulness of the protocol applied. In this work we present
a new scheme for 'growing' macroscopic superposition states of motion of a
mechanical oscillator via cavity quantum optomechanics. The scheme consists of
a series of optical pulses interacting with a mechanical mode via
radiation-pressure followed by photon-counting measurements. The multistep
nature of our protocol allows macroscopic superposition states to be prepared
with a relaxed requirement for the single-photon optomechanical coupling
strength. To demonstrate the feasibility of our scheme, we quantify how initial
mechanical thermal occupation and decoherence affects the non-classicality and
macroscopicity of the states generated. We show that under realistic
experimental conditions, mechanical quantum states can exhibit significant
non-classicality and can be grown to a macroscopic scale.
