  We present high-resolution observations of a sample of 75 K2 targets from
Campaigns 1-3 using speckle interferometry on the Southern Astrophysical
Research (SOAR) telescope and adaptive optics (AO) imaging at the Keck II
telescope. The median SOAR $I$-band and Keck $K_s$-band detection limits at 1"
were $\Delta m_{I}=4.4$~mag and $\Delta m_{K_s}=6.1$~mag, respectively. This
sample includes 37 stars likely to host planets, 32 targets likely to be
eclipsing binaries (EBs), and 6 other targets previously labeled as likely
planetary false positives. We find nine likely physically bound companion stars
within 3" of three candidate transiting exoplanet host stars and six likely
EBs. Six of the nine detected companions are new discoveries; one of the six,
EPIC 206061524, is associated with a planet candidate. Among the EB candidates,
companions were only found near the shortest period ones ($P<3$ days), which is
in line with previous results showing high multiplicity near short-period
binary stars. This high-resolution data, including both the detected companions
and the limits on potential unseen companions, will be useful in future planet
vetting and stellar multiplicity rate studies for planets and binaries.
