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K2 observations of the weak-lined T Tauri binary V928 Tau A+B show the detection of a single, asymmetric eclipse which may be due to a previously unknown substellar companion eclipsing one component of the binary with an orbital period $>$ 66 days. Over an interval of about 9 hours, one component of the binary dims by around 60%, returning to its normal brightness about 5 hours later. From modeling of the eclipse shape we find evidence that the eclipsing companion may be surrounded by a disk or a vast ring system. The modeled disk has a radius of $0.9923\,\pm\,0.0005\,R_*$, with an inclination of $56.78\,\pm\, 0.03^\circ$, a tilt of $41.22\,\pm\,0.05^\circ$, an impact parameter of $-0.2506\,\pm\,0.0002\,R_*$ and an opacity of 1.00. The occulting disk must also move at a transverse velocity of $6.637\,\pm\,0.002\,R_*\,\mathrm{day}^{-1}$, which depending on whether it orbits V928 Tau A or B, corresponds to approximately 73.53 or 69.26 $\mathrm{km s}^{-1}$. A search in ground based archival data reveals additional dimming events, some of which suggest periodicity, but no unambiguous period associated with the eclipse observed by K2. We present a new epoch of astrometry which is used to further refine the orbit of the binary, presenting a new lower bound of 67 years, and constraints on the possible orbital periods of the eclipsing companion. The binary is also separated by 18" ($\sim$2250 au) from the lower mass CFHT-BD-Tau 7, which is likely associated with V928 Tau A+B. We also present new high dispersion optical spectroscopy that we use to characterize the unresolved stellar binary.