Plasma lensing events can have significant observational consequences, including flux modulations and perturbations in pulse arrival times. In this paper we develop and apply a formalism based on an extension of geometric optics that can be used to describe the effects of two dimensional plasma lenses of arbitrary shape. We apply insights from catastrophe theory and the study of uniform asymptotic expansions of integrals to describe the lensing amplification close to fold caustics and in shadow regions, and explore the effects of image appearance and disappearance at caustics in the TOA perturbations due to lensing. We find that the enhanced geometric optics approach successfully reproduces the predictions from wave optics, and that it can be efficiently used to simulate multifrequency TOA residuals during lensing events. Lensing will introduce perturbations in these residuals that will manifest as an increased spreading in the data points at lower frequencies, and will deviate from the expected dispersive $\nu -2$ scaling most significantly when including observations at low frequencies, GHz.