  Recently, using conditioning approaches on the high-harmonic generation
process induced by intense laser-atom interactions, we have developed a new
method for the generation of optical Schr\"odinger cat states (M. Lewenstein et
al., arXiv:2008.10221 (2020)). These quantum optical states have been proven to
be very manageable as, by modifying the conditions under which harmonics are
generated, one can interplay between $\textit{kitten}$ and $\textit{genuine
cat}$ states. Here, we demonstrate that this method can also be used for the
development of new schemes towards the creation of optical Schr\"odinger cat
states, consisting of the superposition of three distinct coherent states.
Apart from the interest these kind of states have on their own, we additionally
propose a scheme for using them towards the generation of large cat states
involving the sum of two different coherent states. The quantum properties of
the obtained superpositions aim to significantly increase the applicability of
optical Schr\"odinger cat states for quantum technology and quantum information
processing.
