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 with pyramid wave-front 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 ~2 and 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 (~10-75 M 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 the James Webb Space Telescope to search for smaller-mass companions below the NIRC2 detection limits.