We quantify the frequency of companions of low redshift ($0.013 < z < 0.0252$), dwarf galaxies ($2 times 10^8$ M$_odot <$ M$_{*} < 5 times 10^9$ M$_odot$) that are isolated from more massive galaxies in SDSS and compare against cosmological expectations using mock observations of the Illustris simulation. Dwarf multiples are defined as 2 or more dwarfs that have angular separations > 55, projected separations r$_p < 150$ kpc and relative line-of-sight velocities $Delta V_{rm LOS} < 150$ km/s. While the mock catalogs predict a factor of 2 more isolated dwarfs than observed in SDSS, the mean number of observed companions per dwarf is $N_c sim 0.04$, in good agreement with Illustris when accounting for SDSS sensitivity limits. Removing these limits in the mock catalogs predicts $N_csim 0.06$ for future surveys (LSST, DESI), which will be complete to M$_* = 2times 10^8$ M$_odot$. The 3D separations of mock dwarf multiples reveal a contamination fraction of $sim$40% in observations from projection effects. Most isolated multiples are pairs; triples are rare and it is cosmologically improbable that bound groups of dwarfs with more than 3 members exist within the parameter range probed in this study. We find that $<$1% of LMC-analogs in the field have an SMC-analog companion. The fraction of dwarf Major Pairs (stellar mass ratio $>$1:4) steadily increases with decreasing Primary stellar mass, whereas the cosmological Major Merger rate (per Gyr) has the opposite behaviour. We conclude that cosmological simulations can be reliably used to constrain the fraction of dwarf mergers across cosmic time.
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