We present results from a resolved stellar population search for dwarf satellite galaxies of six nearby (D $<5$ Mpc), sub-Milky-Way mass hosts using deep ($msim27$ mag) optical imaging from the Large Binocular Telescope. We perform image simulations to quantify our detection efficiency for dwarfs over a large range in luminosity and size, and develop a fast catalog-based emulator that includes a treatment of unresolved photometric blending. We discover no new dwarf satellites, but we recover two previously known dwarfs (DDO 113 and LV J1228+4358) with $M_{text{V}}<-12$ that lie in our survey volume. We preview a new theoretical framework to predict satellite luminosity functions using analytic probability distribution functions and apply it to our sample, finding that we predict one fewer classical dwarf and one more faint dwarf ($M_{text{V}}sim-7.5$) than we find in our observational sample (i.e., the observational sample is slightly top-heavy). However, the overall number of dwarfs in the observational sample (2) is in good agreement with the theoretical expectations. Interestingly, DDO 113 shows signs of environmental quenching and LV J1228+4358 is tidally disrupting, suggesting that low-mass hosts may affect their satellites more severely than previously believed.
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