We extend our investigation of backgrounds to new physics signals, following CMS's data-driven search for supersymmetry at the LHC. The aim is to use different sets of cuts in gamma + 3-jet production to predict the irreducible Z + 3-jet background (with the Z boson decaying to neutrinos) to searches with missing transverse energy + 3-jet signal topologies. We compute ratios of Z + 3-jet to gamma + 3-jet production cross sections and kinematic distributions at next-to-leading order (NLO) in alpha_s. We compare these ratios with those obtained using a parton shower matched to leading-order matrix elements (ME+PS). This study extends our previous work [arXiv:1106.1423 [hep-ph]] on the Z + 2-jet to gamma + 2-jet ratio. We find excellent agreement with the ratio determined from the earlier NLO results involving two instead of three jets, and agreement to within 10% between the NLO and ME+PS results for the ratios. We also examine the possibility of large QCD logarithms in these processes. Ratios of Z + n-jet to gamma + n-jet cross sections are plausibly less sensitive to such corrections than the cross sections themselves. Their effect on estimates of Z + 3-jet to gamma + 3-jet ratios can be assessed experimentally by measuring the gamma + 3-jet to gamma + 2-jet production ratio in search regions. We partially address the question of potentially large electroweak logarithms by computing the real-emission part of the electroweak corrections to the ratio using ME+PS, and find that it is 1% or less. Our estimate of the remaining theoretical uncertainties in the Z to gamma ratio is in agreement with our earlier study.

32 pages, 10 figures, 8 tables, RevTeX