We perform an analytic and numerical study of parametric resonance in a three-neutrino framework for sub-GeV neutrinos which travel through a periodic density profile. Commensurate with the initial level of approximation, we develop a parametric resonance condition similar to the exact condition for two-neutrino systems. For a castle-wall density profile, the oscillation probability is enhanced significantly and bounded by . The phase enters into the oscillation probability as a phase shift. For several cases, we examine the interplay between the characteristics of the castle-wall profile and the phase and determine which profiles maximize the separation between oscillations with . We also consider neutrinos which travel along a chord through the Earth, passing from the mantle to core and back to mantle again. Significant enhancement of the oscillation probability is seen even in the case in which the neutrino energy is far from the MSW resonant energies. At 500 GeV, the difference between oscillation probabilities with and is maximized.