  Most observed stars are part of a multiple star system, but the formation of
such systems and the role of environment and various physical processes is
still poorly understood. We present a suite of radiation-magnetohydrodynamic
simulations of star-forming molecular clouds from the STARFORGE project that
include stellar feedback with varied initial surface density, magnetic fields,
level of turbulence, metallicity, interstellar radiation field, simulation
geometry and turbulent driving. In our fiducial cloud the raw simulation data
reproduces the observed multiplicity fractions for Solar-type and higher mass
stars, similar to previous works. However, after correcting for observational
incompleteness the simulation under-predicts these values. The discrepancy is
likely due to the lack of disk fragmentation, as the simulation only resolves
multiples that form either through capture or core fragmentation. The raw mass
distribution of companions is consistent with randomly drawing from the initial
mass function for the companions of $>1\,\mathrm{M_\odot}$ stars, however,
accounting for observational incompleteness produces a flatter distribution
similar to observations. We show that stellar multiplicity changes as the cloud
evolves and anti-correlates with stellar density. This relationship also
explains most multiplicity variations between runs, i.e., variations in the
initial conditions that increase stellar density (increased surface density,
reduced turbulence) decrease multiplicity. While other parameters, such as
metallicity, interstellar radiation, and geometry significantly affect the star
formation history or the IMF, varying them produces no clear trend in stellar
multiplicity properties.
