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We present new observations of four closely spaced near-ultraviolet (NUV) transits of the hot Jupiter-like exoplanet WASP-12b using Hubble Space Telescope (HST)/Cosmic Origins Spectrograph (COS), significantly increasing the phase resolution of the observed NUV light curve relative to previous observations, while minimizing the temporal variation of the system. We observe significant excess NUV absorption during the transit, with mean normalized in-transit fluxes of , i.e., 2–5σ deeper than the optical transit level of for a uniform stellar disk (the exact confidence level depending on the normalization method used). We further observe an asymmetric transit shape, such that the post-conjunction fluxes are overall 2–3σ higher than pre-conjunction values, and characterized by rapid variations in count rate between the pre-conjunction and out-of-transit levels. We do not find evidence for an early ingress to the NUV transit as suggested by earlier HST observations. However, we show that the NUV count rate observed prior to the optical transit is highly variable, but overall 2.2–3.0σ below the post-transit values and comparable in depth to the optical transit, possibly forming a variable region of NUV absorption from at least phase , limited by the data coverage. [ABSTRACT FROM AUTHOR]