  Non-Gaussian quantum states are crucial to fault-tolerant quantum computation
with continuous-variable systems. Usually, generation of such states involves
trade-offs between success probability and quality of the resultant state. For
example, injecting squeezed light into a multimode interferometer and
postselecting on certain patterns of photon-number outputs in all but one mode,
a fundamentally probabilistic task, can herald the creation of cat states,
Gottesman-Kitaev-Preskill (GKP) states, and more. We consider the addition of a
non-Gaussian resource state, particularly single photons, to this configuration
and show how it improves the qualities and generation probabilities of desired
states. With only two modes, adding a single photon source improves GKP-state
fidelity from 0.68 to 0.95 and adding a second then increases the success
probability eightfold; for cat states with a fixed target fidelity, the
probability of success can be improved by factors of up to 4 by adding
single-photon sources. These demonstrate the usefulness of additional
commonplace non-Gaussian resources for generating desirable states of light.
