  We present the results of a multiplicity survey for a magnitude-limited
sample of 31 classical Be stars conducted with the Navy Precision Optical
Interferometer and the Mark III Stellar Interferometer. The interferometric
observations were used to detect companions in ten previously known binary
systems. For two of these sources (66 Oph and $\beta$ Cep) new orbital
solutions were obtained, while for a third source ($\upsilon$ Sgr) our
observations provide the first direct, visual detection of the hot sdO
companion to the Be primary star. Combining our interferometric observations
with an extensive literature search, we conclude that an additional four
sources (o Cas, 15 Mon, $\beta$ Lyr, and $\beta$ Cep) also contain wider binary
components that are physical companions to the narrow binaries, thus forming
hierarchical multiple systems. Among the sources not previously confirmed as
spectroscopic or visual binaries, BK Cam was resolved on a number of nights
within a close physical proximity of another star with relative motion possibly
suggesting a physical binary. Combining our interferometric observations with
an extensive literature search, we provide a detailed listing of companions
known around each star in the sample, and discuss the multiplicity frequency in
the sample. We also discuss the prospects for future multiplicity studies of
classical Be stars by long baseline optical interferometry.
