Observations of Pluto and its solar-tidal stability zone were made using the Advanced Camera for Surveys (ACS) Wide Field Channel (WFC) on the Hubble Space Telescope on UT 2005 May 15 and May 18. Two small satellites of Pluto, provisionally designated S/2005 P1 and S/2005 P2, were discovered, as discussed by Weaver et al. and Stern et al. Confirming observations of the newly discovered moons were obtained using the ACS in the High Resolution Channel (HRC) mode on 2006 February 15 (Mutchler et al.). Both sets of observations provide strong constraints on the existence of any additional satellites in the Pluto system. Based on the 2005 May observations using the ACS WFC, we place a 90% confidence lower limit of mV=26.8 (mV=27.4 for a 50% confidence lower limit) on the magnitude of undiscovered satellites greater than 5" (1.1×105 km) from Pluto. Using the 2005 February 15 ACS HRC observations we place 90% confidence lower limits on the apparent magnitude of any additional satellites of mV=26.4 between 3" and 5" (6.9×104-1.1×105 km) from Pluto, mV=25.7 between 1" and 3" (2.3×104-6.9×104 km) from Pluto, and mV=24 between 0.3" and 1" (6.9×103-2.3×104 km) from Pluto. The 90% confidence magnitude limits translate into upper limits on the diameters of undiscovered satellites of 29 km outside of 5" from Pluto, 36 km between 3" and 5" from Pluto, 49 km between 1" and 3" from Pluto, and 115 km between 0.3" and 1" for a comet-like albedo of pV=0.04. If potential satellites are assumed to have a Charon-like albedo of pV=0.38, the diameter limits are 9, 12, 16, and 37 km, respectively.