  We present deep Keck/NIRC2 1.6 and 3.8 $\mu m$ imaging of Fomalhaut to
constrain the near-infrared (IR) brightness of Fomalhaut b, recently confirmed
as a likely planet (Currie et al. 2012a), and search for additional planets at
r_proj = 15--150 AU. Using advanced/novel PSF subtraction techniques, we
identify seven candidate substellar companions at projected separations
comparable to Fomalhaut b. However, multi-epoch data shows them to be
background objects. We set a new 3-$\sigma$ upper limit for Fomalhaut b's
H-band brightness of m(H) $\sim$ 23.15 or 1.5 to 4.5 M_J, depending on the
system age and planet cooling models used. We do not recover the possible point
source reported from Spitzer/IRAC data: at its location detection limits are
similar to those for Fomalhaut b. Our data when combined with other recent work
rule out planets with masses and projected separations comparable to HR 8799
bcde and planets with masses M $>$ 3 M_{J} at r_proj $>$ 45 AU. The James Webb
Space Telescope will likely be required to shed substantial further light on
Fomalhaut's planetary system.
