We have used in situ polar Kerr ellipticity measurements to study the perpendicular magnetic behavior of MBE-grown Pd/Co/TM sandwich structures, where TM is the nonmagnetic transition metal overlayer Pd, Cu, or Ag. These structures are epitaxially deposited on thick Pd (111) buffer layers grown on Co-seeded GaAs (110) substrates. Hysteresis curves were measured in situ for systematically varied Co and TM layer thicknesses 2 angstrom less-than-or-equal-to t(Co) less-than-or-equal-to 10 angstrom and 0 angstrom less-than-or-equal-to t(TM) less-than-or-equal-to 200 angstrom. We observed perpendicular loops with a coercive field of H(c) less-than-or-equal-to 200 Oe for the uncovered Co films for t(Co) less-than-or-equal-to 6 angstrom, becoming in-plane above this thickness. However, subsequent deposition of just one atomic layer (almost-equal-to 2 angstrom) of any of the TM over the Co resulted in strongly perpendicular, square hysteresis curves with H(c) greater-than-or-equal-to 700 Oe for all films in the Co thickness range studied. Deposition of TM overlayers causes nonmonotonic behavior in H(c) as a function of coverage. We find a peak in H(c) at a TM coverage of t(TM) almost-equal-to 1.5 angstrom for all materials, with a subsequent monotonic increase above t(TM) almost-equal-to 4 angstrom to a limiting value by t(TM) almost-equal-to 100 angstrom. The peak is most pronounced for Cu, where H(c) changes by more than 200%.