We present new near-IR observations of 76 Class I/flat-spectrum objects in the nearby (d<~320 pc) Perseus, Taurus, Chamaeleon I and II, ρ Ophiuchi, and Serpens dark clouds. These observations are part of a larger systematic infrared multiplicity survey of self-embedded objects in the nearest dark clouds. When combined with the results of our previously published near-infrared multiplicity survey, we find a restricted companion star fraction of 14/79 (18%+/-4%) of the sources surveyed to be binary or higher order multiple systems over a separation range of ~300-2000 AU with a magnitude difference ∆K<=4 and with no correction for background contamination or completeness. This is consistent with the fraction of binary/multiple systems found among older pre-main-sequence T Tauri stars in each of the Taurus, ρ Oph, and Chamaeleon star-forming regions over a similar separation range, as well as the combined companion star fraction for these regions. However, the companion star fraction for solar-type, and lower mass M dwarf, main-sequence stars in the solar neighborhood in this separation range (11%+/-3%) is approximately one-half that of our sample. Together with multiplicity statistics derived for previously published samples of Class 0 and Class I sources, our study suggests that a significant number of binary/multiple objects may remain to be discovered at smaller separations among our Class I/flat-spectrum sample and/or most of the evolution of binary/multiple systems occurs during the Class 0 phase of early stellar evolution.