Exoplanets orbiting pre-main sequence stars are laboratories for studying planet evolution processes, including atmospheric loss, orbital migration, and radiative cooling. V1298 Tau, a young solar analog with an age of 23 $pm$ 4 Myr, is one such laboratory. The star is already known to host a Jupiter-sized planet on a 24 day orbit. Here, we report the discovery of three additional planets --- all between the size of Neptune and Saturn --- based on our analysis of K2 Campaign 4 photometry. Planets c and d have sizes of 5.6 and 6.4 $R_oplus$, respectively and with orbital periods of 8.25 and 12.40 days reside 0.25% outside of the nominal 3:2 mean-motion resonance. Planet e is 8.7 $R_oplus$ in size but only transited once in the K2 time series and thus has a period longer than 36 days, but likely shorter than 223 days. The V1298 Tau system may be a precursor to the compact multiplanet systems found to be common by the Kepler mission. However, the large planet sizes stand in sharp contrast to the vast majority of Kepler multis which have planets smaller than 3 $R_oplus$. Simple dynamical arguments suggest total masses of $<$28 $M_oplus$ and $<$120 $M_oplus$ for the c-d and d-b planet pairs, respectively. The implied low masses suggest that the planets may still be radiatively cooling and contracting, and perhaps losing atmosphere. The V1298 Tau system offers rich prospects for further follow-up including atmospheric characterization by transmission or eclipse spectroscopy, dynamical characterization through transit-timing variations, and measurements of planet masses and obliquities by radial velocities.
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