  The Subaru telescope is currently performing a strategic program (SSP) using
the high-precision near-infrared (NIR) spectrometer IRD to search for
exoplanets around nearby mid/late-M~dwarfs via radial velocity (RV) monitoring.
As part of the observing strategy for the exoplanet survey, signatures of
massive companions such as RV trends are used to reduce the priority of those
stars. However, this RV information remains useful for studying the stellar
multiplicity of nearby M~dwarfs. To search for companions around such
``deprioritized" M~dwarfs, we observed 14 IRD-SSP targets using Keck/NIRC2
observations with pyramid wavefront sensing at NIR wavelengths, leading to high
sensitivity to substellar-mass companions within a few arcseconds. We detected
two new companions (LSPM~J1002+1459~B and LSPM~J2204+1505~B) and two new
candidates that are likely companions (LSPM~J0825+6902~B and LSPM~J1645+0444~B)
as well as one known companion. Including two known companions resolved by the
IRD fiber injection module camera, we detected seven (four new) companions at
projected separations between $\sim2-20$~au in total. A comparison of the
colors with the spectral library suggests that LSPM~J2204+1505~B and
LSPM~J0825+6902~B are located at the boundary between late-M and early-L
spectral types. Our deep high-contrast imaging for targets where no bright
companions were resolved did not reveal any additional companion candidates.
The NIRC2 detection limits could constrain potential substellar-mass companions
($\sim10-75\ M_{\rm Jup}$) at 10~au or further. The failure with Keck/NIRC2
around the IRD-SSP stars having significant RV trends makes these objects
promising targets for further RV monitoring or deeper imaging with JWST to
search for smaller-mass companions below the NIRC2 detection limits.
