Intermediate mass galaxies (IMGs) between 10^9<M/MSun<10^10 occupy an intriguing mass regime where the predicted impact of stellar feedback may dominate their evolution. This includes shaping their dark matter profiles, star formation histories (SFHs), and morphological structure. We test some of these predictions with a large sample of IMGs from CIMGALS in the COSMOS field at 0.3<z<0.4, utilizing high-resolution HST imaging and superb SEDs, among other properties. We have also obtained Magellan IMACS spectroscopy for a subset of ~1000 IMGs, which will lead to constraints on burstiness in their recent SFHs, a key driver in some feedback models.