We present time series photometry and constraints on additional planets in five of the exoplanetary systems studied by the EPOCh (Extrasolar Planet Observation and Characterization) component of the NASA EPOXI mission: HAT-P-4, TrES-3, TrES-2, WASP-3, and HAT-P-7. We conduct a search of the high-precision time series for photometric transits of additional planets. We find no candidate transits with significance higher than our detection limit. From Monte Carlo tests of the time series using putative periods from 0.5 days to 7 days, we demonstrate the sensitivity to detect Neptune-sized companions around TrES-2, sub-Saturn-sized companions in the HAT-P-4, TrES-3, and WASP-3 systems, and Saturn-sized companions around HAT-P-7. We investigate in particular our sensitivity to additional transits in the dynamically favorable 3:2 and 2:1 exterior resonances with the known exoplanets: if we assume coplanar orbits with the known planets, then companions in these resonances with HAT-P-4b, WASP-3b, and HAT-P-7b would be expected to transit, and we can set lower limits on the radii of companions in these systems. In the nearly grazing exoplanetary systems TrES-3 and TrES-2, additional coplanar planets in these resonances are not expected to transit. However, we place lower limits on the radii of companions that would transit if the orbits were misaligned by 2.0 degrees and 1.4 degrees for TrES-3 and TrES-2, respectively.