  Wolf 359 (CN Leo, GJ 406, Gaia DR3 3864972938605115520) is a low-mass star in
the fifth-closest neighboring system (2.41 pc). Because of its relative youth
and proximity, Wolf 359 offers a unique opportunity to study substellar
companions around M stars using infrared high-contrast imaging and radial
velocity monitoring. We present the results of Ms-band (4.67 $\mu$m) vector
vortex coronagraphic imaging using Keck-NIRC2 and add 12 Keck-HIRES velocities
and 68 MAROON-X velocities to the radial velocity baseline. Our analysis
incorporates these data alongside literature radial velocities from CARMENES,
HARPS, and Keck-HIRES to rule out the existence of a close ($a < 10$ AU)
stellar or brown dwarf companion and the majority of large gas-giant
companions. Our survey does not refute or confirm the long-period radial
velocity candidate Wolf 359 b ($P\sim2900$ d) but rules out the candidate's
existence as a large gas-giant ($>4 M_{jup}$) assuming an age of younger than 1
Gyr. We discuss the performance of our high-contrast imaging survey to aid
future observers using Keck-NIRC2 in conjunction with the vortex coronagraph in
the Ms-band and conclude by exploring the direct imaging capabilities with JWST
to observe Jupiter-mass and Neptune-mass planets around Wolf 359.
