  Disposing of simple and efficient sources for photonic states with
non-classical photon statistics is of paramount importance for implementing
quantum computation and communication protocols. In this work, we propose an
innovative approach that drastically simplifies the preparation of non-Gaussian
states as compared to previous proposals, by taking advantage from the
multiplexing capabilities offered by modern quantum photonics tools. Our
proposal is inspired by iterative protocols, where multiple resources are
combined one after the other for obtaining high-amplitude complex output
states. Here, conversely, a large part of the protocol is performed in
parallel, by using a single projective measurement along a mode which partially
overlaps with all the input modes. We show that our protocol can be used to
generate high-quality and high-amplitude Schr\"odinger cat states as well as
more complex states such as error-correcting codes. Remarkably, our proposal
can be implemented with experimentally available resources, highlighting its
straightforward feasibility.
